KILLED proof of input_wdRc0GK75W.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 5 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 7898 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 5 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 71 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 2100 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 3349 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 2125 ms] (30) typed CpxTrs (31) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (32) CdtProblem (33) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRelTRS (37) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (38) CpxTRS (39) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CpxWeightedTrs (41) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CpxTypedWeightedTrs (43) CompletionProof [UPPER BOUND(ID), 0 ms] (44) CpxTypedWeightedCompleteTrs (45) NarrowingProof [BOTH BOUNDS(ID, ID), 126 ms] (46) CpxTypedWeightedCompleteTrs (47) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (48) CpxRNTS (49) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxRNTS (51) CompletionProof [UPPER BOUND(ID), 0 ms] (52) CpxTypedWeightedCompleteTrs (53) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (54) CpxRNTS (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (104) CdtProblem (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 83 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 67 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 100 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 98 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (162) CdtProblem (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 112 ms] (168) CdtProblem (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (186) CdtProblem (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms] (190) CdtProblem (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (196) CdtProblem (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (200) CdtProblem (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 98 ms] (202) CdtProblem (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (204) CdtProblem (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (206) CdtProblem (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (208) CdtProblem (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 139 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 84 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 130 ms] (218) CdtProblem (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms] (220) CdtProblem (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 80 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 154 ms] (226) CdtProblem (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (228) CdtProblem (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms] (230) CdtProblem (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (232) CdtProblem (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms] (234) CdtProblem (235) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 5 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 141 ms] (238) CdtProblem (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (240) CdtProblem (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 111 ms] (242) CdtProblem (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 49 ms] (244) CdtProblem (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 205 ms] (246) CdtProblem (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 53 ms] (248) CdtProblem (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 133 ms] (250) CdtProblem (251) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (252) CdtProblem (253) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (254) CpxWeightedTrs (255) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (256) CpxTypedWeightedTrs (257) CompletionProof [UPPER BOUND(ID), 0 ms] (258) CpxTypedWeightedCompleteTrs (259) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (260) CpxTypedWeightedCompleteTrs (261) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] (262) CpxRNTS (263) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (264) CpxRNTS (265) CompletionProof [UPPER BOUND(ID), 0 ms] (266) CpxTypedWeightedCompleteTrs (267) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (268) CpxRNTS ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) a__g(0) -> s(0) a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(0, cons(X, Y)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__g(X) -> g(X) a__sel(X1, X2) -> sel(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) a__g(0') -> s(0') a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(0', cons(X, Y)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0') -> 0' mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__g(X) -> g(X) a__sel(X1, X2) -> sel(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) a__g(0) -> s(0) a__g(s(X)) -> s(s(a__g(mark(X)))) a__sel(0, cons(X, Y)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(f(X)) -> a__f(mark(X)) mark(g(X)) -> a__g(mark(X)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__f(X) -> f(X) a__g(X) -> g(X) a__sel(X1, X2) -> sel(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0) -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0) -> c14 MARK(s(z0)) -> c15(MARK(z0)) S tuples: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0) -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0) -> c14 MARK(s(z0)) -> c15(MARK(z0)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__G_1, A__SEL_2, MARK_1 Compound Symbols: c_1, c1, c2, c3_2, c4, c5_1, c6_2, c7_2, c8, c9_2, c10_2, c11_2, c12_2, c13_1, c14, c15_1 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0) -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0) -> c14 MARK(s(z0)) -> c15(MARK(z0)) The (relative) TRS S consists of the following rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) The (relative) TRS S consists of the following rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__F, MARK, A__G, mark, A__SEL, a__f, a__g, a__sel They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G mark < MARK MARK = A__SEL mark < A__G A__G = A__SEL mark < A__SEL mark = a__f mark = a__g mark = a__sel a__f = a__g a__f = a__sel a__g = a__sel ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: a__f, A__F, MARK, A__G, mark, A__SEL, a__g, a__sel They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G mark < MARK MARK = A__SEL mark < A__G A__G = A__SEL mark < A__SEL mark = a__f mark = a__g mark = a__sel a__f = a__g a__f = a__sel a__g = a__sel ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_0':s:cons:f:g:sel6_16(n9184_16)) -> gen_0':s:cons:f:g:sel6_16(n9184_16), rt in Omega(0) Induction Base: mark(gen_0':s:cons:f:g:sel6_16(0)) ->_R^Omega(0) 0' Induction Step: mark(gen_0':s:cons:f:g:sel6_16(+(n9184_16, 1))) ->_R^Omega(0) s(mark(gen_0':s:cons:f:g:sel6_16(n9184_16))) ->_IH s(gen_0':s:cons:f:g:sel6_16(c9185_16)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n9184_16)) -> gen_0':s:cons:f:g:sel6_16(n9184_16), rt in Omega(0) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: a__g, A__F, MARK, A__G, A__SEL, a__f, a__sel They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G mark < MARK MARK = A__SEL mark < A__G A__G = A__SEL mark < A__SEL mark = a__f mark = a__g mark = a__sel a__f = a__g a__f = a__sel a__g = a__sel ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) Induction Base: a__g(gen_0':s:cons:f:g:sel6_16(0)) ->_R^Omega(0) s(0') Induction Step: a__g(gen_0':s:cons:f:g:sel6_16(+(n10640_16, 1))) ->_R^Omega(0) s(s(a__g(mark(gen_0':s:cons:f:g:sel6_16(n10640_16))))) ->_L^Omega(0) s(s(a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)))) ->_IH s(s(gen_0':s:cons:f:g:sel6_16(+(1, *(2, c10641_16))))) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (18) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n9184_16)) -> gen_0':s:cons:f:g:sel6_16(n9184_16), rt in Omega(0) a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: a__sel, A__F, MARK, A__G, mark, A__SEL, a__f They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G mark < MARK MARK = A__SEL mark < A__G A__G = A__SEL mark < A__SEL mark = a__f mark = a__g mark = a__sel a__f = a__g a__f = a__sel a__g = a__sel ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_0':s:cons:f:g:sel6_16(n11394_16)) -> gen_0':s:cons:f:g:sel6_16(n11394_16), rt in Omega(0) Induction Base: mark(gen_0':s:cons:f:g:sel6_16(0)) ->_R^Omega(0) 0' Induction Step: mark(gen_0':s:cons:f:g:sel6_16(+(n11394_16, 1))) ->_R^Omega(0) s(mark(gen_0':s:cons:f:g:sel6_16(n11394_16))) ->_IH s(gen_0':s:cons:f:g:sel6_16(c11395_16)) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (20) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n11394_16)) -> gen_0':s:cons:f:g:sel6_16(n11394_16), rt in Omega(0) a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: MARK, A__F, A__G, A__SEL They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G MARK = A__SEL A__G = A__SEL ---------------------------------------- (21) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_0':s:cons:f:g:sel6_16(+(1, n12854_16))) -> *10_16, rt in Omega(n12854_16) Induction Base: MARK(gen_0':s:cons:f:g:sel6_16(+(1, 0))) Induction Step: MARK(gen_0':s:cons:f:g:sel6_16(+(1, +(n12854_16, 1)))) ->_R^Omega(1) c15(MARK(gen_0':s:cons:f:g:sel6_16(+(1, n12854_16)))) ->_IH c15(*10_16) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (22) Complex Obligation (BEST) ---------------------------------------- (23) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n11394_16)) -> gen_0':s:cons:f:g:sel6_16(n11394_16), rt in Omega(0) a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: MARK, A__F, A__G, A__SEL They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G MARK = A__SEL A__G = A__SEL ---------------------------------------- (24) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (25) BOUNDS(n^1, INF) ---------------------------------------- (26) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n11394_16)) -> gen_0':s:cons:f:g:sel6_16(n11394_16), rt in Omega(0) a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) MARK(gen_0':s:cons:f:g:sel6_16(+(1, n12854_16))) -> *10_16, rt in Omega(n12854_16) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: A__F, A__G, A__SEL They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G MARK = A__SEL A__G = A__SEL ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: A__G(gen_0':s:cons:f:g:sel6_16(n39820_16)) -> *10_16, rt in Omega(n39820_16) Induction Base: A__G(gen_0':s:cons:f:g:sel6_16(0)) Induction Step: A__G(gen_0':s:cons:f:g:sel6_16(+(n39820_16, 1))) ->_R^Omega(1) c3(A__G(mark(gen_0':s:cons:f:g:sel6_16(n39820_16))), MARK(gen_0':s:cons:f:g:sel6_16(n39820_16))) ->_L^Omega(0) c3(A__G(gen_0':s:cons:f:g:sel6_16(n39820_16)), MARK(gen_0':s:cons:f:g:sel6_16(n39820_16))) ->_IH c3(*10_16, MARK(gen_0':s:cons:f:g:sel6_16(n39820_16))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n11394_16)) -> gen_0':s:cons:f:g:sel6_16(n11394_16), rt in Omega(0) a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) MARK(gen_0':s:cons:f:g:sel6_16(+(1, n12854_16))) -> *10_16, rt in Omega(n12854_16) A__G(gen_0':s:cons:f:g:sel6_16(n39820_16)) -> *10_16, rt in Omega(n39820_16) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: A__SEL, A__F, MARK They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G MARK = A__SEL A__G = A__SEL ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_0':s:cons:f:g:sel6_16(+(1, n125968_16))) -> *10_16, rt in Omega(n125968_16) Induction Base: MARK(gen_0':s:cons:f:g:sel6_16(+(1, 0))) Induction Step: MARK(gen_0':s:cons:f:g:sel6_16(+(1, +(n125968_16, 1)))) ->_R^Omega(1) c15(MARK(gen_0':s:cons:f:g:sel6_16(+(1, n125968_16)))) ->_IH c15(*10_16) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) Obligation: Innermost TRS: Rules: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0') -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0', cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0') -> c14 MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0') -> s(0') a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0', cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) Types: A__F :: 0':s:cons:f:g:sel -> c:c1 c :: c9:c10:c11:c12:c13:c14:c15 -> c:c1 MARK :: 0':s:cons:f:g:sel -> c9:c10:c11:c12:c13:c14:c15 c1 :: c:c1 A__G :: 0':s:cons:f:g:sel -> c2:c3:c4 0' :: 0':s:cons:f:g:sel c2 :: c2:c3:c4 s :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c3 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c2:c3:c4 mark :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c4 :: c2:c3:c4 A__SEL :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> c5:c6:c7:c8 cons :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c6 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c7 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c5:c6:c7:c8 c8 :: c5:c6:c7:c8 f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c9 :: c:c1 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c10 :: c2:c3:c4 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel c11 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c12 :: c5:c6:c7:c8 -> c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c13 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 c14 :: c9:c10:c11:c12:c13:c14:c15 c15 :: c9:c10:c11:c12:c13:c14:c15 -> c9:c10:c11:c12:c13:c14:c15 a__f :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__g :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel a__sel :: 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel -> 0':s:cons:f:g:sel hole_c:c11_16 :: c:c1 hole_0':s:cons:f:g:sel2_16 :: 0':s:cons:f:g:sel hole_c9:c10:c11:c12:c13:c14:c153_16 :: c9:c10:c11:c12:c13:c14:c15 hole_c2:c3:c44_16 :: c2:c3:c4 hole_c5:c6:c7:c85_16 :: c5:c6:c7:c8 gen_0':s:cons:f:g:sel6_16 :: Nat -> 0':s:cons:f:g:sel gen_c9:c10:c11:c12:c13:c14:c157_16 :: Nat -> c9:c10:c11:c12:c13:c14:c15 gen_c2:c3:c48_16 :: Nat -> c2:c3:c4 gen_c5:c6:c7:c89_16 :: Nat -> c5:c6:c7:c8 Lemmas: mark(gen_0':s:cons:f:g:sel6_16(n11394_16)) -> gen_0':s:cons:f:g:sel6_16(n11394_16), rt in Omega(0) a__g(gen_0':s:cons:f:g:sel6_16(n10640_16)) -> gen_0':s:cons:f:g:sel6_16(+(1, *(2, n10640_16))), rt in Omega(0) MARK(gen_0':s:cons:f:g:sel6_16(+(1, n125968_16))) -> *10_16, rt in Omega(n125968_16) A__G(gen_0':s:cons:f:g:sel6_16(n39820_16)) -> *10_16, rt in Omega(n39820_16) Generator Equations: gen_0':s:cons:f:g:sel6_16(0) <=> 0' gen_0':s:cons:f:g:sel6_16(+(x, 1)) <=> s(gen_0':s:cons:f:g:sel6_16(x)) gen_c9:c10:c11:c12:c13:c14:c157_16(0) <=> c14 gen_c9:c10:c11:c12:c13:c14:c157_16(+(x, 1)) <=> c9(c(c14), gen_c9:c10:c11:c12:c13:c14:c157_16(x)) gen_c2:c3:c48_16(0) <=> c2 gen_c2:c3:c48_16(+(x, 1)) <=> c3(gen_c2:c3:c48_16(x), c14) gen_c5:c6:c7:c89_16(0) <=> c5(c14) gen_c5:c6:c7:c89_16(+(x, 1)) <=> c6(gen_c5:c6:c7:c89_16(x), c14) The following defined symbols remain to be analysed: A__F They will be analysed ascendingly in the following order: A__F = MARK A__F = A__G A__F = A__SEL MARK = A__G MARK = A__SEL A__G = A__SEL ---------------------------------------- (31) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0) -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0) -> c14 MARK(s(z0)) -> c15(MARK(z0)) S tuples: A__F(z0) -> c(MARK(z0)) A__F(z0) -> c1 A__G(0) -> c2 A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__G(z0) -> c4 A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) A__SEL(z0, z1) -> c8 MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(0) -> c14 MARK(s(z0)) -> c15(MARK(z0)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__G_1, A__SEL_2, MARK_1 Compound Symbols: c_1, c1, c2, c3_2, c4, c5_1, c6_2, c7_2, c8, c9_2, c10_2, c11_2, c12_2, c13_1, c14, c15_1 ---------------------------------------- (33) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: A__F(z0) -> c1 A__G(0) -> c2 A__SEL(z0, z1) -> c8 A__G(z0) -> c4 MARK(0) -> c14 ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) S tuples: A__F(z0) -> c(MARK(z0)) A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__G_1, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_2, c5_1, c6_2, c7_2, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1 ---------------------------------------- (35) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (36) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) The (relative) TRS S consists of the following rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Rewrite Strategy: INNERMOST ---------------------------------------- (37) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (38) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (39) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (40) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) [1] A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) [1] A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) [1] MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) [1] MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c13(MARK(z0)) [1] MARK(s(z0)) -> c15(MARK(z0)) [1] a__f(z0) -> cons(mark(z0), f(g(z0))) [0] a__f(z0) -> f(z0) [0] a__g(0) -> s(0) [0] a__g(s(z0)) -> s(s(a__g(mark(z0)))) [0] a__g(z0) -> g(z0) [0] a__sel(0, cons(z0, z1)) -> mark(z0) [0] a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) [0] a__sel(z0, z1) -> sel(z0, z1) [0] mark(f(z0)) -> a__f(mark(z0)) [0] mark(g(z0)) -> a__g(mark(z0)) [0] mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (41) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (42) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) [1] A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) [1] A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) [1] MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) [1] MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c13(MARK(z0)) [1] MARK(s(z0)) -> c15(MARK(z0)) [1] a__f(z0) -> cons(mark(z0), f(g(z0))) [0] a__f(z0) -> f(z0) [0] a__g(0) -> s(0) [0] a__g(s(z0)) -> s(s(a__g(mark(z0)))) [0] a__g(z0) -> g(z0) [0] a__sel(0, cons(z0, z1)) -> mark(z0) [0] a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) [0] a__sel(z0, z1) -> sel(z0, z1) [0] mark(f(z0)) -> a__f(mark(z0)) [0] mark(g(z0)) -> a__g(mark(z0)) [0] mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] The TRS has the following type information: A__F :: s:0:cons:f:g:sel -> c c :: c9:c10:c11:c12:c13:c15 -> c MARK :: s:0:cons:f:g:sel -> c9:c10:c11:c12:c13:c15 A__G :: s:0:cons:f:g:sel -> c3 s :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c3 :: c3 -> c9:c10:c11:c12:c13:c15 -> c3 mark :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel A__SEL :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> c5:c6:c7 0 :: s:0:cons:f:g:sel cons :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c15 -> c5:c6:c7 c6 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c5:c6:c7 c7 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c5:c6:c7 f :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c9 :: c -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 g :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c10 :: c3 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 sel :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel c11 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c12 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c13 :: c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c15 :: c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 a__f :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel a__g :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel a__sel :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel Rewrite Strategy: INNERMOST ---------------------------------------- (43) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__F_1 A__G_1 A__SEL_2 MARK_1 (c) The following functions are completely defined: a__f_1 a__g_1 a__sel_2 mark_1 Due to the following rules being added: a__f(v0) -> 0 [0] a__g(v0) -> 0 [0] a__sel(v0, v1) -> 0 [0] mark(v0) -> 0 [0] And the following fresh constants: const, const1, const2, const3 ---------------------------------------- (44) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) [1] A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) [1] A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) [1] MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) [1] MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c13(MARK(z0)) [1] MARK(s(z0)) -> c15(MARK(z0)) [1] a__f(z0) -> cons(mark(z0), f(g(z0))) [0] a__f(z0) -> f(z0) [0] a__g(0) -> s(0) [0] a__g(s(z0)) -> s(s(a__g(mark(z0)))) [0] a__g(z0) -> g(z0) [0] a__sel(0, cons(z0, z1)) -> mark(z0) [0] a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) [0] a__sel(z0, z1) -> sel(z0, z1) [0] mark(f(z0)) -> a__f(mark(z0)) [0] mark(g(z0)) -> a__g(mark(z0)) [0] mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] a__f(v0) -> 0 [0] a__g(v0) -> 0 [0] a__sel(v0, v1) -> 0 [0] mark(v0) -> 0 [0] The TRS has the following type information: A__F :: s:0:cons:f:g:sel -> c c :: c9:c10:c11:c12:c13:c15 -> c MARK :: s:0:cons:f:g:sel -> c9:c10:c11:c12:c13:c15 A__G :: s:0:cons:f:g:sel -> c3 s :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c3 :: c3 -> c9:c10:c11:c12:c13:c15 -> c3 mark :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel A__SEL :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> c5:c6:c7 0 :: s:0:cons:f:g:sel cons :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c15 -> c5:c6:c7 c6 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c5:c6:c7 c7 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c5:c6:c7 f :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c9 :: c -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 g :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c10 :: c3 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 sel :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel c11 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c12 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c13 :: c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c15 :: c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 a__f :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel a__g :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel a__sel :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel const :: c const1 :: c9:c10:c11:c12:c13:c15 const2 :: c3 const3 :: c5:c6:c7 Rewrite Strategy: INNERMOST ---------------------------------------- (45) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (46) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) [1] A__G(s(f(z0'))) -> c3(A__G(a__f(mark(z0'))), MARK(f(z0'))) [1] A__G(s(g(z0''))) -> c3(A__G(a__g(mark(z0''))), MARK(g(z0''))) [1] A__G(s(sel(z01, z1'))) -> c3(A__G(a__sel(mark(z01), mark(z1'))), MARK(sel(z01, z1'))) [1] A__G(s(cons(z02, z1''))) -> c3(A__G(cons(mark(z02), z1'')), MARK(cons(z02, z1''))) [1] A__G(s(0)) -> c3(A__G(0), MARK(0)) [1] A__G(s(s(z03))) -> c3(A__G(s(mark(z03))), MARK(s(z03))) [1] A__G(s(z0)) -> c3(A__G(0), MARK(z0)) [1] A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) [1] MARK(f(f(z084))) -> c9(A__F(a__f(mark(z084))), MARK(f(z084))) [1] MARK(f(g(z085))) -> c9(A__F(a__g(mark(z085))), MARK(g(z085))) [1] MARK(f(sel(z086, z133))) -> c9(A__F(a__sel(mark(z086), mark(z133))), MARK(sel(z086, z133))) [1] MARK(f(cons(z087, z134))) -> c9(A__F(cons(mark(z087), z134)), MARK(cons(z087, z134))) [1] MARK(f(0)) -> c9(A__F(0), MARK(0)) [1] MARK(f(s(z088))) -> c9(A__F(s(mark(z088))), MARK(s(z088))) [1] MARK(f(z0)) -> c9(A__F(0), MARK(z0)) [1] MARK(g(f(z089))) -> c10(A__G(a__f(mark(z089))), MARK(f(z089))) [1] MARK(g(g(z090))) -> c10(A__G(a__g(mark(z090))), MARK(g(z090))) [1] MARK(g(sel(z091, z135))) -> c10(A__G(a__sel(mark(z091), mark(z135))), MARK(sel(z091, z135))) [1] MARK(g(cons(z092, z136))) -> c10(A__G(cons(mark(z092), z136)), MARK(cons(z092, z136))) [1] MARK(g(0)) -> c10(A__G(0), MARK(0)) [1] MARK(g(s(z093))) -> c10(A__G(s(mark(z093))), MARK(s(z093))) [1] MARK(g(z0)) -> c10(A__G(0), MARK(z0)) [1] MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c13(MARK(z0)) [1] MARK(s(z0)) -> c15(MARK(z0)) [1] a__f(z0) -> cons(mark(z0), f(g(z0))) [0] a__f(z0) -> f(z0) [0] a__g(0) -> s(0) [0] a__g(s(f(z0174))) -> s(s(a__g(a__f(mark(z0174))))) [0] a__g(s(g(z0175))) -> s(s(a__g(a__g(mark(z0175))))) [0] a__g(s(sel(z0176, z169))) -> s(s(a__g(a__sel(mark(z0176), mark(z169))))) [0] a__g(s(cons(z0177, z170))) -> s(s(a__g(cons(mark(z0177), z170)))) [0] a__g(s(0)) -> s(s(a__g(0))) [0] a__g(s(s(z0178))) -> s(s(a__g(s(mark(z0178))))) [0] a__g(s(z0)) -> s(s(a__g(0))) [0] a__g(z0) -> g(z0) [0] a__sel(0, cons(z0, z1)) -> mark(z0) [0] a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) [0] a__sel(z0, z1) -> sel(z0, z1) [0] mark(f(f(z0219))) -> a__f(a__f(mark(z0219))) [0] mark(f(g(z0220))) -> a__f(a__g(mark(z0220))) [0] mark(f(sel(z0221, z187))) -> a__f(a__sel(mark(z0221), mark(z187))) [0] mark(f(cons(z0222, z188))) -> a__f(cons(mark(z0222), z188)) [0] mark(f(0)) -> a__f(0) [0] mark(f(s(z0223))) -> a__f(s(mark(z0223))) [0] mark(f(z0)) -> a__f(0) [0] mark(g(f(z0224))) -> a__g(a__f(mark(z0224))) [0] mark(g(g(z0225))) -> a__g(a__g(mark(z0225))) [0] mark(g(sel(z0226, z189))) -> a__g(a__sel(mark(z0226), mark(z189))) [0] mark(g(cons(z0227, z190))) -> a__g(cons(mark(z0227), z190)) [0] mark(g(0)) -> a__g(0) [0] mark(g(s(z0228))) -> a__g(s(mark(z0228))) [0] mark(g(z0)) -> a__g(0) [0] mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] a__f(v0) -> 0 [0] a__g(v0) -> 0 [0] a__sel(v0, v1) -> 0 [0] mark(v0) -> 0 [0] The TRS has the following type information: A__F :: s:0:cons:f:g:sel -> c c :: c9:c10:c11:c12:c13:c15 -> c MARK :: s:0:cons:f:g:sel -> c9:c10:c11:c12:c13:c15 A__G :: s:0:cons:f:g:sel -> c3 s :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c3 :: c3 -> c9:c10:c11:c12:c13:c15 -> c3 mark :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel A__SEL :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> c5:c6:c7 0 :: s:0:cons:f:g:sel cons :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel c5 :: c9:c10:c11:c12:c13:c15 -> c5:c6:c7 c6 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c5:c6:c7 c7 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c5:c6:c7 f :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c9 :: c -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 g :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel c10 :: c3 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 sel :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel c11 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c12 :: c5:c6:c7 -> c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c13 :: c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 c15 :: c9:c10:c11:c12:c13:c15 -> c9:c10:c11:c12:c13:c15 a__f :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel a__g :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel a__sel :: s:0:cons:f:g:sel -> s:0:cons:f:g:sel -> s:0:cons:f:g:sel const :: c const1 :: c9:c10:c11:c12:c13:c15 const2 :: c3 const3 :: c5:c6:c7 Rewrite Strategy: INNERMOST ---------------------------------------- (47) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: A__F(z) -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0 A__G(z) -{ 1 }-> 1 + A__G(a__sel(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z = 1 + (1 + z01 + z1'), z01 >= 0, z1' >= 0 A__G(z) -{ 1 }-> 1 + A__G(a__g(mark(z0''))) + MARK(1 + z0'') :|: z = 1 + (1 + z0''), z0'' >= 0 A__G(z) -{ 1 }-> 1 + A__G(a__f(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 A__G(z) -{ 1 }-> 1 + A__G(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__G(z) -{ 1 }-> 1 + A__G(0) + MARK(0) :|: z = 1 + 0 A__G(z) -{ 1 }-> 1 + A__G(1 + mark(z03)) + MARK(1 + z03) :|: z = 1 + (1 + z03), z03 >= 0 A__G(z) -{ 1 }-> 1 + A__G(1 + mark(z02) + z1'') + MARK(1 + z02 + z1'') :|: z = 1 + (1 + z02 + z1''), z02 >= 0, z1'' >= 0 A__SEL(z, z') -{ 1 }-> 1 + MARK(z0) :|: z' = 1 + z0 + z1, z1 >= 0, z0 >= 0, z = 0 A__SEL(z, z') -{ 1 }-> 1 + A__SEL(mark(z0), mark(z2)) + MARK(z0) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__SEL(z, z') -{ 1 }-> 1 + A__SEL(mark(z0), mark(z2)) + MARK(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__SEL(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__SEL(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__G(a__sel(mark(z091), mark(z135))) + MARK(1 + z091 + z135) :|: z091 >= 0, z135 >= 0, z = 1 + (1 + z091 + z135) MARK(z) -{ 1 }-> 1 + A__G(a__g(mark(z090))) + MARK(1 + z090) :|: z = 1 + (1 + z090), z090 >= 0 MARK(z) -{ 1 }-> 1 + A__G(a__f(mark(z089))) + MARK(1 + z089) :|: z089 >= 0, z = 1 + (1 + z089) MARK(z) -{ 1 }-> 1 + A__G(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__G(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__G(1 + mark(z093)) + MARK(1 + z093) :|: z = 1 + (1 + z093), z093 >= 0 MARK(z) -{ 1 }-> 1 + A__G(1 + mark(z092) + z136) + MARK(1 + z092 + z136) :|: z092 >= 0, z = 1 + (1 + z092 + z136), z136 >= 0 MARK(z) -{ 1 }-> 1 + A__F(a__sel(mark(z086), mark(z133))) + MARK(1 + z086 + z133) :|: z = 1 + (1 + z086 + z133), z133 >= 0, z086 >= 0 MARK(z) -{ 1 }-> 1 + A__F(a__g(mark(z085))) + MARK(1 + z085) :|: z = 1 + (1 + z085), z085 >= 0 MARK(z) -{ 1 }-> 1 + A__F(a__f(mark(z084))) + MARK(1 + z084) :|: z = 1 + (1 + z084), z084 >= 0 MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__F(1 + mark(z088)) + MARK(1 + z088) :|: z088 >= 0, z = 1 + (1 + z088) MARK(z) -{ 1 }-> 1 + A__F(1 + mark(z087) + z134) + MARK(1 + z087 + z134) :|: z134 >= 0, z = 1 + (1 + z087 + z134), z087 >= 0 a__f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__f(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__f(z) -{ 0 }-> 1 + mark(z0) + (1 + (1 + z0)) :|: z = z0, z0 >= 0 a__g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__g(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__g(z) -{ 0 }-> 1 + 0 :|: z = 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(a__sel(mark(z0176), mark(z169)))) :|: z = 1 + (1 + z0176 + z169), z169 >= 0, z0176 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(a__g(mark(z0175)))) :|: z = 1 + (1 + z0175), z0175 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(a__f(mark(z0174)))) :|: z0174 >= 0, z = 1 + (1 + z0174) a__g(z) -{ 0 }-> 1 + (1 + a__g(0)) :|: z = 1 + 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(0)) :|: z = 1 + z0, z0 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(1 + mark(z0178))) :|: z0178 >= 0, z = 1 + (1 + z0178) a__g(z) -{ 0 }-> 1 + (1 + a__g(1 + mark(z0177) + z170)) :|: z170 >= 0, z0177 >= 0, z = 1 + (1 + z0177 + z170) a__sel(z, z') -{ 0 }-> mark(z0) :|: z' = 1 + z0 + z1, z1 >= 0, z0 >= 0, z = 0 a__sel(z, z') -{ 0 }-> a__sel(mark(z0), mark(z2)) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__sel(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__sel(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__g(a__sel(mark(z0226), mark(z189))) :|: z = 1 + (1 + z0226 + z189), z189 >= 0, z0226 >= 0 mark(z) -{ 0 }-> a__g(a__g(mark(z0225))) :|: z = 1 + (1 + z0225), z0225 >= 0 mark(z) -{ 0 }-> a__g(a__f(mark(z0224))) :|: z = 1 + (1 + z0224), z0224 >= 0 mark(z) -{ 0 }-> a__g(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__g(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__g(1 + mark(z0228)) :|: z0228 >= 0, z = 1 + (1 + z0228) mark(z) -{ 0 }-> a__g(1 + mark(z0227) + z190) :|: z190 >= 0, z = 1 + (1 + z0227 + z190), z0227 >= 0 mark(z) -{ 0 }-> a__f(a__sel(mark(z0221), mark(z187))) :|: z187 >= 0, z0221 >= 0, z = 1 + (1 + z0221 + z187) mark(z) -{ 0 }-> a__f(a__g(mark(z0220))) :|: z0220 >= 0, z = 1 + (1 + z0220) mark(z) -{ 0 }-> a__f(a__f(mark(z0219))) :|: z0219 >= 0, z = 1 + (1 + z0219) mark(z) -{ 0 }-> a__f(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__f(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__f(1 + mark(z0223)) :|: z = 1 + (1 + z0223), z0223 >= 0 mark(z) -{ 0 }-> a__f(1 + mark(z0222) + z188) :|: z = 1 + (1 + z0222 + z188), z0222 >= 0, z188 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (49) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: A__F(z) -{ 1 }-> 1 + MARK(z) :|: z >= 0 A__G(z) -{ 1 }-> 1 + A__G(a__sel(mark(z01), mark(z1'))) + MARK(1 + z01 + z1') :|: z = 1 + (1 + z01 + z1'), z01 >= 0, z1' >= 0 A__G(z) -{ 1 }-> 1 + A__G(a__g(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__G(z) -{ 1 }-> 1 + A__G(a__f(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__G(z) -{ 1 }-> 1 + A__G(0) + MARK(0) :|: z = 1 + 0 A__G(z) -{ 1 }-> 1 + A__G(0) + MARK(z - 1) :|: z - 1 >= 0 A__G(z) -{ 1 }-> 1 + A__G(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 A__G(z) -{ 1 }-> 1 + A__G(1 + mark(z02) + z1'') + MARK(1 + z02 + z1'') :|: z = 1 + (1 + z02 + z1''), z02 >= 0, z1'' >= 0 A__SEL(z, z') -{ 1 }-> 1 + MARK(z0) :|: z' = 1 + z0 + z1, z1 >= 0, z0 >= 0, z = 0 A__SEL(z, z') -{ 1 }-> 1 + A__SEL(mark(z - 1), mark(z2)) + MARK(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__SEL(z, z') -{ 1 }-> 1 + A__SEL(mark(z - 1), mark(z2)) + MARK(z - 1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__SEL(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__SEL(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__G(a__sel(mark(z091), mark(z135))) + MARK(1 + z091 + z135) :|: z091 >= 0, z135 >= 0, z = 1 + (1 + z091 + z135) MARK(z) -{ 1 }-> 1 + A__G(a__g(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__G(a__f(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__G(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__G(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__G(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__G(1 + mark(z092) + z136) + MARK(1 + z092 + z136) :|: z092 >= 0, z = 1 + (1 + z092 + z136), z136 >= 0 MARK(z) -{ 1 }-> 1 + A__F(a__sel(mark(z086), mark(z133))) + MARK(1 + z086 + z133) :|: z = 1 + (1 + z086 + z133), z133 >= 0, z086 >= 0 MARK(z) -{ 1 }-> 1 + A__F(a__g(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(a__f(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__F(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__F(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__F(1 + mark(z087) + z134) + MARK(1 + z087 + z134) :|: z134 >= 0, z = 1 + (1 + z087 + z134), z087 >= 0 a__f(z) -{ 0 }-> 0 :|: z >= 0 a__f(z) -{ 0 }-> 1 + z :|: z >= 0 a__f(z) -{ 0 }-> 1 + mark(z) + (1 + (1 + z)) :|: z >= 0 a__g(z) -{ 0 }-> 0 :|: z >= 0 a__g(z) -{ 0 }-> 1 + z :|: z >= 0 a__g(z) -{ 0 }-> 1 + 0 :|: z = 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(a__sel(mark(z0176), mark(z169)))) :|: z = 1 + (1 + z0176 + z169), z169 >= 0, z0176 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(a__g(mark(z - 2)))) :|: z - 2 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(a__f(mark(z - 2)))) :|: z - 2 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(0)) :|: z = 1 + 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(0)) :|: z - 1 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(1 + mark(z - 2))) :|: z - 2 >= 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(1 + mark(z0177) + z170)) :|: z170 >= 0, z0177 >= 0, z = 1 + (1 + z0177 + z170) a__sel(z, z') -{ 0 }-> mark(z0) :|: z' = 1 + z0 + z1, z1 >= 0, z0 >= 0, z = 0 a__sel(z, z') -{ 0 }-> a__sel(mark(z - 1), mark(z2)) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__sel(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__sel(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 mark(z) -{ 0 }-> a__sel(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__g(a__sel(mark(z0226), mark(z189))) :|: z = 1 + (1 + z0226 + z189), z189 >= 0, z0226 >= 0 mark(z) -{ 0 }-> a__g(a__g(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__g(a__f(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__g(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__g(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__g(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__g(1 + mark(z0227) + z190) :|: z190 >= 0, z = 1 + (1 + z0227 + z190), z0227 >= 0 mark(z) -{ 0 }-> a__f(a__sel(mark(z0221), mark(z187))) :|: z187 >= 0, z0221 >= 0, z = 1 + (1 + z0221 + z187) mark(z) -{ 0 }-> a__f(a__g(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__f(a__f(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__f(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__f(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__f(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__f(1 + mark(z0222) + z188) :|: z = 1 + (1 + z0222 + z188), z0222 >= 0, z188 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (51) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__f(v0) -> null_a__f [0] a__g(v0) -> null_a__g [0] a__sel(v0, v1) -> null_a__sel [0] mark(v0) -> null_mark [0] A__G(v0) -> null_A__G [0] A__SEL(v0, v1) -> null_A__SEL [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__f, null_a__g, null_a__sel, null_mark, null_A__G, null_A__SEL, null_MARK, const ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__F(z0) -> c(MARK(z0)) [1] A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) [1] A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) [1] A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) [1] MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) [1] MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) [1] MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) [1] MARK(cons(z0, z1)) -> c13(MARK(z0)) [1] MARK(s(z0)) -> c15(MARK(z0)) [1] a__f(z0) -> cons(mark(z0), f(g(z0))) [0] a__f(z0) -> f(z0) [0] a__g(0) -> s(0) [0] a__g(s(z0)) -> s(s(a__g(mark(z0)))) [0] a__g(z0) -> g(z0) [0] a__sel(0, cons(z0, z1)) -> mark(z0) [0] a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) [0] a__sel(z0, z1) -> sel(z0, z1) [0] mark(f(z0)) -> a__f(mark(z0)) [0] mark(g(z0)) -> a__g(mark(z0)) [0] mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] a__f(v0) -> null_a__f [0] a__g(v0) -> null_a__g [0] a__sel(v0, v1) -> null_a__sel [0] mark(v0) -> null_mark [0] A__G(v0) -> null_A__G [0] A__SEL(v0, v1) -> null_A__SEL [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__F :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> c c :: c9:c10:c11:c12:c13:c15:null_MARK -> c MARK :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> c9:c10:c11:c12:c13:c15:null_MARK A__G :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> c3:null_A__G s :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark c3 :: c3:null_A__G -> c9:c10:c11:c12:c13:c15:null_MARK -> c3:null_A__G mark :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark A__SEL :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> c5:c6:c7:null_A__SEL 0 :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark cons :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark c5 :: c9:c10:c11:c12:c13:c15:null_MARK -> c5:c6:c7:null_A__SEL c6 :: c5:c6:c7:null_A__SEL -> c9:c10:c11:c12:c13:c15:null_MARK -> c5:c6:c7:null_A__SEL c7 :: c5:c6:c7:null_A__SEL -> c9:c10:c11:c12:c13:c15:null_MARK -> c5:c6:c7:null_A__SEL f :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark c9 :: c -> c9:c10:c11:c12:c13:c15:null_MARK -> c9:c10:c11:c12:c13:c15:null_MARK g :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark c10 :: c3:null_A__G -> c9:c10:c11:c12:c13:c15:null_MARK -> c9:c10:c11:c12:c13:c15:null_MARK sel :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark c11 :: c5:c6:c7:null_A__SEL -> c9:c10:c11:c12:c13:c15:null_MARK -> c9:c10:c11:c12:c13:c15:null_MARK c12 :: c5:c6:c7:null_A__SEL -> c9:c10:c11:c12:c13:c15:null_MARK -> c9:c10:c11:c12:c13:c15:null_MARK c13 :: c9:c10:c11:c12:c13:c15:null_MARK -> c9:c10:c11:c12:c13:c15:null_MARK c15 :: c9:c10:c11:c12:c13:c15:null_MARK -> c9:c10:c11:c12:c13:c15:null_MARK a__f :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark a__g :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark a__sel :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark -> s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark null_a__f :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark null_a__g :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark null_a__sel :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark null_mark :: s:0:cons:f:g:sel:null_a__f:null_a__g:null_a__sel:null_mark null_A__G :: c3:null_A__G null_A__SEL :: c5:c6:c7:null_A__SEL null_MARK :: c9:c10:c11:c12:c13:c15:null_MARK const :: c Rewrite Strategy: INNERMOST ---------------------------------------- (53) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 null_a__f => 0 null_a__g => 0 null_a__sel => 0 null_mark => 0 null_A__G => 0 null_A__SEL => 0 null_MARK => 0 const => 0 ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: A__F(z) -{ 1 }-> 1 + MARK(z0) :|: z = z0, z0 >= 0 A__G(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__G(z) -{ 1 }-> 1 + A__G(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 A__SEL(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__SEL(z, z') -{ 1 }-> 1 + MARK(z0) :|: z' = 1 + z0 + z1, z1 >= 0, z0 >= 0, z = 0 A__SEL(z, z') -{ 1 }-> 1 + A__SEL(mark(z0), mark(z2)) + MARK(z0) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__SEL(z, z') -{ 1 }-> 1 + A__SEL(mark(z0), mark(z2)) + MARK(z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__SEL(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__SEL(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__G(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__F(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 a__f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__f(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__f(z) -{ 0 }-> 1 + mark(z0) + (1 + (1 + z0)) :|: z = z0, z0 >= 0 a__g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__g(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__g(z) -{ 0 }-> 1 + 0 :|: z = 0 a__g(z) -{ 0 }-> 1 + (1 + a__g(mark(z0))) :|: z = 1 + z0, z0 >= 0 a__sel(z, z') -{ 0 }-> mark(z0) :|: z' = 1 + z0 + z1, z1 >= 0, z0 >= 0, z = 0 a__sel(z, z') -{ 0 }-> a__sel(mark(z0), mark(z2)) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__sel(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__sel(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__sel(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__g(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__f(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__G(s(z0)) -> c3(A__G(mark(z0)), MARK(z0)) by A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(cons(z0, z1))) -> c3(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__G(s(0)) -> c3(A__G(0), MARK(0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(cons(z0, z1))) -> c3(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__G(s(0)) -> c3(A__G(0), MARK(0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(cons(z0, z1))) -> c3(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__G(s(0)) -> c3(A__G(0), MARK(0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c6_2, c7_2, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__G(s(0)) -> c3(A__G(0), MARK(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(cons(z0, z1))) -> c3(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(cons(z0, z1))) -> c3(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c6_2, c7_2, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c6_2, c7_2, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(z0), cons(z1, z2)) -> c6(A__SEL(mark(z0), mark(z2)), MARK(z0)) by A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c7_2, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c7_2, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(z0), cons(z1, z2)) -> c7(A__SEL(mark(z0), mark(z2)), MARK(z2)) by A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(A__SEL(cons(mark(z0), z1), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c10_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(g(z0)) -> c10(A__G(mark(z0)), MARK(z0)) by MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(cons(z0, z1))) -> c10(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(g(0)) -> c10(A__G(0), MARK(0)) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(cons(z0, z1))) -> c10(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(g(0)) -> c10(A__G(0), MARK(0)) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(cons(z0, z1))) -> c10(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(g(0)) -> c10(A__G(0), MARK(0)) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(g(0)) -> c10(A__G(0), MARK(0)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(cons(z0, z1))) -> c10(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(cons(z0, z1))) -> c10(A__G(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c11_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(z0, z1)) -> c11(A__SEL(mark(z0), mark(z1)), MARK(z0)) by MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, 0)) -> c11(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, s(z0))) -> c11(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c11(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1)), MARK(0)) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, 0)) -> c11(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, s(z0))) -> c11(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c11(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1)), MARK(0)) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, 0)) -> c11(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, s(z0))) -> c11(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c11(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1)), MARK(0)) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c12_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z1)) by MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(0)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__G(s(f(z0))) -> c3(A__G(a__f(mark(z0))), MARK(f(z0))) by A__G(s(f(x0))) -> c3(A__G(cons(mark(mark(x0)), f(g(mark(x0))))), MARK(f(x0))) A__G(s(f(x0))) -> c3(A__G(f(mark(x0))), MARK(f(x0))) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(x0))) -> c3(A__G(cons(mark(mark(x0)), f(g(mark(x0))))), MARK(f(x0))) A__G(s(f(x0))) -> c3(A__G(f(mark(x0))), MARK(f(x0))) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(x0))) -> c3(A__G(cons(mark(mark(x0)), f(g(mark(x0))))), MARK(f(x0))) A__G(s(f(x0))) -> c3(A__G(f(mark(x0))), MARK(f(x0))) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (91) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__G(s(g(z0))) -> c3(A__G(a__g(mark(z0))), MARK(g(z0))) by A__G(s(g(x0))) -> c3(A__G(g(mark(x0))), MARK(g(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(0))) -> c3(A__G(a__g(0)), MARK(g(0))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(x0))) -> c3(A__G(g(mark(x0))), MARK(g(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(0))) -> c3(A__G(a__g(0)), MARK(g(0))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(x0))) -> c3(A__G(g(mark(x0))), MARK(g(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(0))) -> c3(A__G(a__g(0)), MARK(g(0))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (95) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__G(s(sel(z0, z1))) -> c3(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) by A__G(s(sel(x0, x1))) -> c3(A__G(sel(mark(x0), mark(x1))), MARK(sel(x0, x1))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, x1))) -> c3(A__G(sel(mark(x0), mark(x1))), MARK(sel(x0, x1))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, x1))) -> c3(A__G(sel(mark(x0), mark(x1))), MARK(sel(x0, x1))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_2, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__G(s(s(z0))) -> c3(A__G(s(mark(z0))), MARK(s(z0))) by A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(0))) -> c3(A__G(s(0)), MARK(s(0))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(0))) -> c3(A__G(s(0)), MARK(s(0))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(0))) -> c3(A__G(s(0)), MARK(s(0))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (101) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (103) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, f(z0))) -> c6(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) by A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), f(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__f(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2))), MARK(0)) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), f(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__f(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2))), MARK(0)) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), f(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__f(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2))), MARK(0)) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (105) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (107) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, g(z0))) -> c6(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) by A__SEL(s(x0), cons(x1, g(x2))) -> c6(A__SEL(mark(x0), g(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__g(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2))), MARK(0)) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(A__SEL(mark(x0), g(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__g(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2))), MARK(0)) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(A__SEL(mark(x0), g(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__g(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2))), MARK(0)) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), 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c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), 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z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c6(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) by A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(A__SEL(mark(x0), sel(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__sel(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(A__SEL(mark(x0), sel(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__sel(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> 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x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), 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MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(A__SEL(mark(x0), sel(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__sel(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) by A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), cons(mark(x2), x3)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, 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c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), cons(mark(x2), x3)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), cons(mark(x2), x3)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(f(z0)), cons(x1, x2)) -> c6(A__SEL(a__f(mark(z0)), mark(x2)), MARK(f(z0))) by A__SEL(s(f(x0)), cons(x1, f(z0))) -> c6(A__SEL(a__f(mark(x0)), a__f(mark(z0))), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, g(z0))) -> c6(A__SEL(a__f(mark(x0)), a__g(mark(z0))), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, sel(z0, z1))) -> c6(A__SEL(a__f(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, cons(z0, z1))) -> c6(A__SEL(a__f(mark(x0)), cons(mark(z0), z1)), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(A__SEL(a__f(mark(x0)), 0), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(A__SEL(f(mark(x0)), mark(x2)), MARK(f(x0))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), 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A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, 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mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(A__SEL(a__f(mark(x0)), 0), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(A__SEL(f(mark(x0)), mark(x2)), MARK(f(x0))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), 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c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, 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g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(g(z0)), cons(x1, x2)) -> c6(A__SEL(a__g(mark(z0)), mark(x2)), MARK(g(z0))) by A__SEL(s(g(x0)), cons(x1, f(z0))) -> c6(A__SEL(a__g(mark(x0)), a__f(mark(z0))), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, g(z0))) -> c6(A__SEL(a__g(mark(x0)), a__g(mark(z0))), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, sel(z0, z1))) -> c6(A__SEL(a__g(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, cons(z0, z1))) -> c6(A__SEL(a__g(mark(x0)), cons(mark(z0), z1)), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(A__SEL(a__g(mark(x0)), 0), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(A__SEL(g(mark(x0)), mark(x2)), MARK(g(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2)), MARK(g(0))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(A__SEL(a__g(mark(x0)), 0), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(A__SEL(g(mark(x0)), mark(x2)), MARK(g(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2)), MARK(g(0))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(A__SEL(a__g(mark(x0)), 0), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(A__SEL(g(mark(x0)), mark(x2)), MARK(g(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2)), MARK(g(0))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(sel(z0, z1))) by A__SEL(s(sel(x0, x1)), cons(x2, f(z0))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), a__f(mark(z0))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, g(z0))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), a__g(mark(z0))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, sel(z0, z1))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, cons(z0, z1))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(sel(x0, x1))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(sel(x0, x1))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(sel(x0, x1))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(s(z0)), cons(x1, x2)) -> c6(A__SEL(s(mark(z0)), mark(x2)), MARK(s(z0))) by A__SEL(s(s(x0)), cons(x1, f(z0))) -> c6(A__SEL(s(mark(x0)), a__f(mark(z0))), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, g(z0))) -> c6(A__SEL(s(mark(x0)), a__g(mark(z0))), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, sel(z0, z1))) -> c6(A__SEL(s(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, cons(z0, z1))) -> c6(A__SEL(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(A__SEL(s(mark(x0)), 0), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(x0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> 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c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(A__SEL(s(mark(x0)), 0), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(x0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(A__SEL(s(mark(x0)), 0), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(x0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2))) by A__SEL(s(0), cons(x0, f(z0))) -> c6(A__SEL(0, a__f(mark(z0)))) A__SEL(s(0), cons(x0, g(z0))) -> c6(A__SEL(0, a__g(mark(z0)))) A__SEL(s(0), cons(x0, sel(z0, z1))) -> c6(A__SEL(0, a__sel(mark(z0), mark(z1)))) A__SEL(s(0), cons(x0, cons(z0, z1))) -> c6(A__SEL(0, cons(mark(z0), z1))) A__SEL(s(0), cons(x0, 0)) -> c6(A__SEL(0, 0)) A__SEL(s(0), cons(x0, s(z0))) -> c6(A__SEL(0, s(mark(z0)))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(0), cons(x0, 0)) -> c6(A__SEL(0, 0)) A__SEL(s(0), cons(x0, s(z0))) -> c6(A__SEL(0, s(mark(z0)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(0), cons(x0, 0)) -> c6(A__SEL(0, 0)) A__SEL(s(0), cons(x0, s(z0))) -> c6(A__SEL(0, s(mark(z0)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (137) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(0), cons(x0, 0)) -> c6(A__SEL(0, 0)) A__SEL(s(0), cons(x0, s(z0))) -> c6(A__SEL(0, s(mark(z0)))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, f(z0))) -> c7(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) by A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, g(z0))) -> c7(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) by A__SEL(s(x0), cons(x1, g(x2))) -> c7(A__SEL(mark(x0), g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0)), MARK(g(0))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(A__SEL(mark(x0), g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0)), MARK(g(0))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), 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A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(A__SEL(mark(x0), g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0)), MARK(g(0))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, sel(z0, z1))) -> c7(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) by A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(A__SEL(mark(x0), sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(A__SEL(mark(x0), sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(A__SEL(mark(x0), sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> 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A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c7(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, 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A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), 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MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(f(z0)), cons(x1, x2)) -> c7(A__SEL(a__f(mark(z0)), mark(x2)), MARK(x2)) by A__SEL(s(f(x0)), cons(x1, f(z0))) -> c7(A__SEL(a__f(mark(x0)), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(f(x0)), cons(x1, g(z0))) -> c7(A__SEL(a__f(mark(x0)), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(f(x0)), cons(x1, sel(z0, z1))) -> c7(A__SEL(a__f(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(f(x0)), cons(x1, cons(z0, z1))) -> c7(A__SEL(a__f(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(f(x0)), cons(x1, 0)) -> c7(A__SEL(a__f(mark(x0)), 0), MARK(0)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(f(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(x0)), cons(x1, 0)) -> c7(A__SEL(a__f(mark(x0)), 0), MARK(0)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(f(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(x0)), cons(x1, 0)) -> c7(A__SEL(a__f(mark(x0)), 0), MARK(0)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(f(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(f(x0)), cons(x1, 0)) -> c7(A__SEL(a__f(mark(x0)), 0), MARK(0)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(f(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(A__SEL(f(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), 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A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, 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c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(g(z0)), cons(x1, x2)) -> c7(A__SEL(a__g(mark(z0)), mark(x2)), MARK(x2)) by A__SEL(s(g(x0)), cons(x1, f(z0))) -> c7(A__SEL(a__g(mark(x0)), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(g(x0)), cons(x1, g(z0))) -> c7(A__SEL(a__g(mark(x0)), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(g(x0)), cons(x1, sel(z0, z1))) -> c7(A__SEL(a__g(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(g(x0)), cons(x1, cons(z0, z1))) -> c7(A__SEL(a__g(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(g(x0)), cons(x1, 0)) -> c7(A__SEL(a__g(mark(x0)), 0), MARK(0)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(A__SEL(g(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), 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c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) 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c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> 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z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> 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mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, 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c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> 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a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(x0)), cons(x1, 0)) -> c7(A__SEL(a__g(mark(x0)), 0), MARK(0)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(A__SEL(g(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (163) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(g(x0)), cons(x1, 0)) -> c7(A__SEL(a__g(mark(x0)), 0), MARK(0)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(A__SEL(g(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(A__SEL(g(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) S tuples: A__F(z0) -> 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A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(sel(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), mark(x2)), MARK(x2)) by A__SEL(s(sel(x0, x1)), cons(x2, f(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(sel(x0, x1)), cons(x2, g(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(sel(x0, x1)), cons(x2, sel(z0, z1))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(sel(x0, x1)), cons(x2, cons(z0, z1))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(A__SEL(sel(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) by A__SEL(s(0), cons(x0, f(z0))) -> c7(A__SEL(0, a__f(mark(z0))), MARK(f(z0))) A__SEL(s(0), cons(x0, g(z0))) -> c7(A__SEL(0, a__g(mark(z0))), MARK(g(z0))) A__SEL(s(0), cons(x0, sel(z0, z1))) -> c7(A__SEL(0, a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(0), cons(x0, cons(z0, z1))) -> c7(A__SEL(0, cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) 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A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), 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MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> 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A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) by A__SEL(s(s(x0)), cons(x1, f(z0))) -> c7(A__SEL(s(mark(x0)), a__f(mark(z0))), MARK(f(z0))) A__SEL(s(s(x0)), cons(x1, g(z0))) -> c7(A__SEL(s(mark(x0)), a__g(mark(z0))), MARK(g(z0))) A__SEL(s(s(x0)), cons(x1, sel(z0, z1))) -> c7(A__SEL(s(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(s(x0)), cons(x1, cons(z0, z1))) -> c7(A__SEL(s(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(s(x0)), cons(x1, 0)) -> c7(A__SEL(s(mark(x0)), 0), MARK(0)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c7(A__SEL(s(mark(x0)), 0), MARK(0)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c7(A__SEL(s(mark(x0)), 0), MARK(0)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(s(x0)), cons(x1, 0)) -> c7(A__SEL(s(mark(x0)), 0), MARK(0)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(g(f(z0))) -> c10(A__G(a__f(mark(z0))), MARK(f(z0))) by MARK(g(f(x0))) -> c10(A__G(cons(mark(mark(x0)), f(g(mark(x0))))), MARK(f(x0))) MARK(g(f(x0))) -> c10(A__G(f(mark(x0))), MARK(f(x0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), 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MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), 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MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), 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s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(x0))) -> c10(A__G(cons(mark(mark(x0)), f(g(mark(x0))))), MARK(f(x0))) MARK(g(f(x0))) -> c10(A__G(f(mark(x0))), MARK(f(x0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (187) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> 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A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (189) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(g(g(z0))) -> c10(A__G(a__g(mark(z0))), MARK(g(z0))) by MARK(g(g(x0))) -> c10(A__G(g(mark(x0))), MARK(g(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(0))) -> c10(A__G(a__g(0)), MARK(g(0))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, 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A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(x0))) -> c10(A__G(g(mark(x0))), MARK(g(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(0))) -> c10(A__G(a__g(0)), MARK(g(0))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), 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A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(x0))) -> c10(A__G(g(mark(x0))), MARK(g(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(0))) -> c10(A__G(a__g(0)), MARK(g(0))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (191) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), 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MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), 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MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), 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a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (193) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(g(sel(z0, z1))) -> c10(A__G(a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) by MARK(g(sel(x0, x1))) -> c10(A__G(sel(mark(x0), mark(x1))), MARK(sel(x0, x1))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, x1))) -> c10(A__G(sel(mark(x0), mark(x1))), MARK(sel(x0, x1))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, x1))) -> c10(A__G(sel(mark(x0), mark(x1))), MARK(sel(x0, x1))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (195) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> 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MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2 ---------------------------------------- (197) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(g(s(z0))) -> c10(A__G(s(mark(z0))), MARK(s(z0))) by MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(0))) -> c10(A__G(s(0)), MARK(s(0))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(0))) -> c10(A__G(s(0)), MARK(s(0))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), 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MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> 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MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(0))) -> c10(A__G(s(0)), MARK(s(0))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (199) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> 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c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), 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a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (201) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, f(z0))) -> c11(A__SEL(mark(x0), a__f(mark(z0))), MARK(x0)) by MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), f(mark(x1))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), f(x1))) -> c11(A__SEL(cons(mark(z0), z1), a__f(mark(x1))), MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1))), MARK(0)) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), f(mark(x1))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), f(x1))) -> c11(A__SEL(cons(mark(z0), z1), a__f(mark(x1))), MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1))), MARK(0)) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), 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x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), f(mark(x1))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), f(x1))) -> c11(A__SEL(cons(mark(z0), z1), a__f(mark(x1))), MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1))), MARK(0)) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (203) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), 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A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (205) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, g(z0))) -> c11(A__SEL(mark(x0), a__g(mark(z0))), MARK(x0)) by MARK(sel(x0, g(x1))) -> c11(A__SEL(mark(x0), g(mark(x1))), MARK(x0)) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), g(x1))) -> c11(A__SEL(cons(mark(z0), z1), a__g(mark(x1))), MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1))), MARK(0)) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(x1))) -> c11(A__SEL(mark(x0), g(mark(x1))), MARK(x0)) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), g(x1))) -> c11(A__SEL(cons(mark(z0), z1), a__g(mark(x1))), MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1))), MARK(0)) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(x1))) -> c11(A__SEL(mark(x0), g(mark(x1))), MARK(x0)) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), g(x1))) -> c11(A__SEL(cons(mark(z0), z1), a__g(mark(x1))), MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1))), MARK(0)) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (207) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) 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MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (209) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, sel(z0, z1))) -> c11(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) by MARK(sel(x0, sel(x1, x2))) -> c11(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) 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MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) 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-> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, x2))) -> c11(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), 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c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> 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MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), 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c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, cons(z0, z1))) -> c11(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(A__SEL(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2)), MARK(0)) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, 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A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> 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MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), 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c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(A__SEL(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2)), MARK(0)) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, 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MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (217) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(f(z0), x1)) -> c11(A__SEL(a__f(mark(z0)), mark(x1)), MARK(f(z0))) by MARK(sel(f(x0), f(z0))) -> c11(A__SEL(a__f(mark(x0)), a__f(mark(z0))), MARK(f(x0))) MARK(sel(f(x0), g(z0))) -> c11(A__SEL(a__f(mark(x0)), a__g(mark(z0))), MARK(f(x0))) MARK(sel(f(x0), sel(z0, z1))) -> c11(A__SEL(a__f(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(f(x0))) MARK(sel(f(x0), cons(z0, z1))) -> c11(A__SEL(a__f(mark(x0)), cons(mark(z0), z1)), MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(A__SEL(a__f(mark(x0)), 0), MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(f(x0))) MARK(sel(f(x0), x1)) -> c11(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x1)), MARK(f(x0))) MARK(sel(f(x0), x1)) -> c11(A__SEL(f(mark(x0)), mark(x1)), MARK(f(x0))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, 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a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, 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c11(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(f(x0))) MARK(sel(f(x0), x1)) -> c11(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x1)), MARK(f(x0))) MARK(sel(f(x0), x1)) -> c11(A__SEL(f(mark(x0)), mark(x1)), MARK(f(x0))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(x0), 0)) -> c11(A__SEL(a__f(mark(x0)), 0), MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(A__SEL(a__f(mark(x0)), s(mark(z0))), MARK(f(x0))) MARK(sel(f(x0), x1)) -> c11(A__SEL(cons(mark(mark(x0)), f(g(mark(x0)))), mark(x1)), MARK(f(x0))) MARK(sel(f(x0), x1)) -> c11(A__SEL(f(mark(x0)), mark(x1)), MARK(f(x0))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (219) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (221) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(g(z0), x1)) -> c11(A__SEL(a__g(mark(z0)), mark(x1)), MARK(g(z0))) by MARK(sel(g(x0), f(z0))) -> c11(A__SEL(a__g(mark(x0)), a__f(mark(z0))), MARK(g(x0))) MARK(sel(g(x0), g(z0))) -> c11(A__SEL(a__g(mark(x0)), a__g(mark(z0))), MARK(g(x0))) MARK(sel(g(x0), sel(z0, z1))) -> c11(A__SEL(a__g(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(g(x0))) MARK(sel(g(x0), cons(z0, z1))) -> c11(A__SEL(a__g(mark(x0)), cons(mark(z0), z1)), MARK(g(x0))) MARK(sel(g(x0), 0)) -> c11(A__SEL(a__g(mark(x0)), 0), MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(A__SEL(g(mark(x0)), mark(x1)), MARK(g(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1)), MARK(g(0))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(x0), 0)) -> c11(A__SEL(a__g(mark(x0)), 0), MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(A__SEL(g(mark(x0)), mark(x1)), MARK(g(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1)), MARK(g(0))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(x0), 0)) -> c11(A__SEL(a__g(mark(x0)), 0), MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(A__SEL(a__g(mark(x0)), s(mark(z0))), MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(A__SEL(g(mark(x0)), mark(x1)), MARK(g(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1)), MARK(g(0))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), 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c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), 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A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(sel(z0, z1), x1)) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) by MARK(sel(sel(x0, x1), f(z0))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), a__f(mark(z0))), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), g(z0))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), a__g(mark(z0))), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), sel(z0, z1))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), cons(z0, z1))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), 0)) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(A__SEL(sel(mark(x0), mark(x1)), mark(x2)), MARK(sel(x0, x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, x1), 0)) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(A__SEL(sel(mark(x0), mark(x1)), mark(x2)), MARK(sel(x0, x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, x1), 0)) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(A__SEL(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(A__SEL(sel(mark(x0), mark(x1)), mark(x2)), MARK(sel(x0, x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (227) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), 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c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> 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MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), 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A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2 ---------------------------------------- (229) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(s(z0), x1)) -> c11(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(sel(s(x0), f(z0))) -> c11(A__SEL(s(mark(x0)), a__f(mark(z0))), MARK(s(x0))) MARK(sel(s(x0), g(z0))) -> c11(A__SEL(s(mark(x0)), a__g(mark(z0))), MARK(s(x0))) MARK(sel(s(x0), sel(z0, z1))) -> c11(A__SEL(s(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(s(x0))) MARK(sel(s(x0), cons(z0, z1))) -> c11(A__SEL(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(A__SEL(s(mark(x0)), 0), MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) 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MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) 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c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(x0), 0)) -> c11(A__SEL(s(mark(x0)), 0), MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (231) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 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A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) 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A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), 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MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), 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c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (233) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(0, x1)) -> c11(A__SEL(0, mark(x1))) by MARK(sel(0, f(z0))) -> c11(A__SEL(0, a__f(mark(z0)))) MARK(sel(0, g(z0))) -> c11(A__SEL(0, a__g(mark(z0)))) MARK(sel(0, sel(z0, z1))) -> c11(A__SEL(0, a__sel(mark(z0), mark(z1)))) MARK(sel(0, cons(z0, z1))) -> c11(A__SEL(0, cons(mark(z0), z1))) MARK(sel(0, 0)) -> c11(A__SEL(0, 0)) MARK(sel(0, s(z0))) -> c11(A__SEL(0, s(mark(z0)))) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) 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mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(0, 0)) -> c11(A__SEL(0, 0)) MARK(sel(0, s(z0))) -> c11(A__SEL(0, s(mark(z0)))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(0, 0)) -> c11(A__SEL(0, 0)) MARK(sel(0, s(z0))) -> c11(A__SEL(0, s(mark(z0)))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (235) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(sel(0, s(z0))) -> c11(A__SEL(0, s(mark(z0)))) MARK(sel(0, 0)) -> c11(A__SEL(0, 0)) ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> 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MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, f(z0))) -> c12(A__SEL(mark(x0), a__f(mark(z0))), MARK(f(z0))) by MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) 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c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), 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MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) 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c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (239) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, 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MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), 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a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (241) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, g(z0))) -> c12(A__SEL(mark(x0), a__g(mark(z0))), MARK(g(z0))) by MARK(sel(x0, g(x1))) -> c12(A__SEL(mark(x0), g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0)), MARK(g(0))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(cons(z0, z1), g(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, 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A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), 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MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(x1))) -> c12(A__SEL(mark(x0), g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0)), MARK(g(0))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(cons(z0, z1), g(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (243) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), 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MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 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-> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), 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MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (245) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) by MARK(sel(x0, sel(x1, x2))) -> c12(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> 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x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), 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c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), 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MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, 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c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, 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c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, sel(x1, x2))) -> c12(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (247) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), 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A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> 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MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), 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MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(sel(x1, x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> 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A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(sel(x1, x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (249) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(sel(x0, cons(f(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(cons(f(z0), x2))) MARK(sel(x0, cons(g(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(cons(g(z0), x2))) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(sel(x0, cons(0, x2))) -> c12(A__SEL(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(sel(x0, cons(s(z0), x2))) -> c12(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(sel(f(z0), cons(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(g(z0), cons(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(0, cons(x1, x2))) -> c12(A__SEL(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(s(z0), cons(x1, x2))) -> c12(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(x0, cons(x1, x2))) -> c12(MARK(cons(x1, x2))) ---------------------------------------- (250) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), 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mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), 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x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), 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c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) 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c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, 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a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) 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mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(x0, cons(f(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(cons(f(z0), x2))) MARK(sel(x0, cons(g(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(cons(g(z0), x2))) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(sel(x0, cons(0, x2))) -> c12(A__SEL(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(sel(x0, cons(s(z0), x2))) -> c12(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(sel(f(z0), cons(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(g(z0), cons(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(0, cons(x1, x2))) -> c12(A__SEL(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(s(z0), cons(x1, x2))) -> c12(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(x0, cons(x1, x2))) -> c12(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (251) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (252) Obligation: Complexity Dependency Tuples Problem Rules: a__f(z0) -> cons(mark(z0), f(g(z0))) a__f(z0) -> f(z0) a__g(0) -> s(0) a__g(s(z0)) -> s(s(a__g(mark(z0)))) a__g(z0) -> g(z0) a__sel(0, cons(z0, z1)) -> mark(z0) a__sel(s(z0), cons(z1, z2)) -> a__sel(mark(z0), mark(z2)) a__sel(z0, z1) -> sel(z0, z1) mark(f(z0)) -> a__f(mark(z0)) mark(g(z0)) -> a__g(mark(z0)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) Tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> 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c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) MARK(g(s(cons(z0, z1)))) -> c10(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) MARK(g(s(s(z0)))) -> c10(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) MARK(g(s(x0))) -> c10(MARK(s(x0))) MARK(g(s(0))) -> c10(MARK(s(0))) MARK(sel(x0, f(x1))) -> c11(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(x0)) MARK(sel(x0, f(f(z0)))) -> c11(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, f(g(z0)))) -> c11(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, f(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, f(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, f(0))) -> c11(A__SEL(mark(x0), a__f(0)), MARK(x0)) MARK(sel(x0, f(s(z0)))) -> c11(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), f(x1))) -> c11(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), f(x1))) -> c11(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), f(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), f(x1))) -> c11(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(s(z0))) MARK(sel(x0, f(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), f(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, f(x1))) -> c11(A__SEL(0, a__f(mark(x1)))) MARK(sel(x0, g(f(z0)))) -> c11(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, g(g(z0)))) -> c11(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, g(sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, g(cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, g(0))) -> c11(A__SEL(mark(x0), a__g(0)), MARK(x0)) MARK(sel(x0, g(s(z0)))) -> c11(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) MARK(sel(f(z0), g(x1))) -> c11(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(f(z0))) MARK(sel(g(z0), g(x1))) -> c11(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(z0))) MARK(sel(sel(z0, z1), g(x1))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), g(x1))) -> c11(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(s(z0))) MARK(sel(x0, g(x1))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), g(x1))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, g(x1))) -> c11(A__SEL(0, a__g(mark(x1)))) MARK(sel(x0, sel(x1, f(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, g(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c11(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(f(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c11(A__SEL(0, a__sel(mark(x1), mark(x2)))) MARK(sel(x0, cons(f(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(g(z0), x2))) -> c11(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(x0)) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(sel(x0, cons(0, x2))) -> c11(A__SEL(mark(x0), cons(0, x2)), MARK(x0)) MARK(sel(x0, cons(s(z0), x2))) -> c11(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(sel(f(z0), cons(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(f(z0))) MARK(sel(g(z0), cons(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(g(z0))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(sel(s(z0), cons(x1, x2))) -> c11(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(z0, z1))) MARK(sel(0, cons(x1, x2))) -> c11(A__SEL(0, cons(mark(x1), x2))) MARK(sel(f(f(z0)), x1)) -> c11(A__SEL(a__f(a__f(mark(z0))), mark(x1)), MARK(f(f(z0)))) MARK(sel(f(g(z0)), x1)) -> c11(A__SEL(a__f(a__g(mark(z0))), mark(x1)), MARK(f(g(z0)))) MARK(sel(f(sel(z0, z1)), x1)) -> c11(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(f(sel(z0, z1)))) MARK(sel(f(cons(z0, z1)), x1)) -> c11(A__SEL(a__f(cons(mark(z0), z1)), mark(x1)), MARK(f(cons(z0, z1)))) MARK(sel(f(0), x1)) -> c11(A__SEL(a__f(0), mark(x1)), MARK(f(0))) MARK(sel(f(s(z0)), x1)) -> c11(A__SEL(a__f(s(mark(z0))), mark(x1)), MARK(f(s(z0)))) MARK(sel(f(x0), x1)) -> c11(MARK(f(x0))) MARK(sel(f(x0), 0)) -> c11(MARK(f(x0))) MARK(sel(f(x0), s(z0))) -> c11(MARK(f(x0))) MARK(sel(g(f(z0)), x1)) -> c11(A__SEL(a__g(a__f(mark(z0))), mark(x1)), MARK(g(f(z0)))) MARK(sel(g(g(z0)), x1)) -> c11(A__SEL(a__g(a__g(mark(z0))), mark(x1)), MARK(g(g(z0)))) MARK(sel(g(sel(z0, z1)), x1)) -> c11(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(g(sel(z0, z1)))) MARK(sel(g(cons(z0, z1)), x1)) -> c11(A__SEL(a__g(cons(mark(z0), z1)), mark(x1)), MARK(g(cons(z0, z1)))) MARK(sel(g(s(z0)), x1)) -> c11(A__SEL(a__g(s(mark(z0))), mark(x1)), MARK(g(s(z0)))) MARK(sel(g(x0), 0)) -> c11(MARK(g(x0))) MARK(sel(g(x0), s(z0))) -> c11(MARK(g(x0))) MARK(sel(g(x0), x1)) -> c11(MARK(g(x0))) MARK(sel(g(0), x1)) -> c11(A__SEL(a__g(0), mark(x1))) MARK(sel(sel(x0, f(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x2)), MARK(sel(x0, f(z0)))) MARK(sel(sel(x0, g(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x2)), MARK(sel(x0, g(z0)))) MARK(sel(sel(x0, sel(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(sel(sel(x0, cons(z0, z1)), x2)) -> c11(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(sel(sel(x0, 0), x2)) -> c11(A__SEL(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(sel(sel(x0, s(z0)), x2)) -> c11(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(sel(sel(f(z0), x1), x2)) -> c11(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x2)), MARK(sel(f(z0), x1))) MARK(sel(sel(g(z0), x1), x2)) -> c11(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x2)), MARK(sel(g(z0), x1))) MARK(sel(sel(sel(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(sel(sel(cons(z0, z1), x1), x2)) -> c11(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(sel(sel(0, x1), x2)) -> c11(A__SEL(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(sel(sel(s(z0), x1), x2)) -> c11(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(sel(sel(x0, x1), 0)) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), s(z0))) -> c11(MARK(sel(x0, x1))) MARK(sel(sel(x0, x1), x2)) -> c11(MARK(sel(x0, x1))) MARK(sel(s(f(z0)), x1)) -> c11(A__SEL(s(a__f(mark(z0))), mark(x1)), MARK(s(f(z0)))) MARK(sel(s(g(z0)), x1)) -> c11(A__SEL(s(a__g(mark(z0))), mark(x1)), MARK(s(g(z0)))) MARK(sel(s(sel(z0, z1)), x1)) -> c11(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(sel(s(cons(z0, z1)), x1)) -> c11(A__SEL(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(sel(s(0), x1)) -> c11(A__SEL(s(0), mark(x1)), MARK(s(0))) MARK(sel(s(s(z0)), x1)) -> c11(A__SEL(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(sel(s(x0), x1)) -> c11(MARK(s(x0))) MARK(sel(s(x0), 0)) -> c11(MARK(s(x0))) MARK(sel(s(x0), s(z0))) -> c11(MARK(s(x0))) MARK(sel(x0, f(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), f(g(mark(x1))))), MARK(f(x1))) MARK(sel(x0, f(f(z0)))) -> c12(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(sel(x0, f(g(z0)))) -> c12(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(sel(x0, f(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(sel(x0, f(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(sel(x0, f(0))) -> c12(A__SEL(mark(x0), a__f(0)), MARK(f(0))) MARK(sel(x0, f(s(z0)))) -> c12(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(sel(f(z0), f(x1))) -> c12(A__SEL(a__f(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(g(z0), f(x1))) -> c12(A__SEL(a__g(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(sel(z0, z1), f(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(0, f(x1))) -> c12(A__SEL(0, a__f(mark(x1))), MARK(f(x1))) MARK(sel(s(z0), f(x1))) -> c12(A__SEL(s(mark(z0)), a__f(mark(x1))), MARK(f(x1))) MARK(sel(x0, f(x1))) -> c12(MARK(f(x1))) MARK(sel(cons(z0, z1), f(x1))) -> c12(MARK(f(x1))) MARK(sel(x0, g(f(z0)))) -> c12(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(x0, cons(f(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(cons(f(z0), x2))) MARK(sel(x0, cons(g(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(cons(g(z0), x2))) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(sel(x0, cons(0, x2))) -> c12(A__SEL(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(sel(x0, cons(s(z0), x2))) -> c12(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(sel(f(z0), cons(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(g(z0), cons(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(0, cons(x1, x2))) -> c12(A__SEL(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(s(z0), cons(x1, x2))) -> c12(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(x0, cons(x1, x2))) -> c12(MARK(cons(x1, x2))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c12(MARK(cons(x1, x2))) S tuples: A__F(z0) -> c(MARK(z0)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(f(z0)) -> c9(A__F(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c13(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__G(s(cons(z0, z1))) -> c3(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) MARK(g(cons(z0, z1))) -> c10(MARK(cons(z0, z1))) MARK(sel(x0, 0)) -> c11(MARK(x0)) MARK(sel(x0, s(z0))) -> c11(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c11(MARK(cons(z0, z1))) MARK(sel(f(z0), x1)) -> c12(A__SEL(a__f(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(g(z0), x1)) -> c12(A__SEL(a__g(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c12(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(x1)) A__G(s(f(f(z0)))) -> c3(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__G(s(f(g(z0)))) -> c3(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__G(s(f(sel(z0, z1)))) -> c3(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__G(s(f(cons(z0, z1)))) -> c3(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__G(s(f(0))) -> c3(A__G(a__f(0)), MARK(f(0))) A__G(s(f(s(z0)))) -> c3(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) A__G(s(f(x0))) -> c3(MARK(f(x0))) A__G(s(g(f(z0)))) -> c3(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__G(s(g(g(z0)))) -> c3(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__G(s(g(sel(z0, z1)))) -> c3(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__G(s(g(cons(z0, z1)))) -> c3(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__G(s(g(s(z0)))) -> c3(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) A__G(s(g(x0))) -> c3(MARK(g(x0))) A__G(s(g(0))) -> c3(A__G(a__g(0))) A__G(s(sel(x0, f(z0)))) -> c3(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) A__G(s(sel(x0, g(z0)))) -> c3(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) A__G(s(sel(x0, sel(z0, z1)))) -> c3(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) A__G(s(sel(x0, cons(z0, z1)))) -> c3(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) A__G(s(sel(x0, 0))) -> c3(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) A__G(s(sel(x0, s(z0)))) -> c3(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) A__G(s(sel(f(z0), x1))) -> c3(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) A__G(s(sel(g(z0), x1))) -> c3(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) A__G(s(sel(sel(z0, z1), x1))) -> c3(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) A__G(s(sel(cons(z0, z1), x1))) -> c3(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) A__G(s(sel(0, x1))) -> c3(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) A__G(s(sel(s(z0), x1))) -> c3(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) A__G(s(sel(x0, x1))) -> c3(MARK(sel(x0, x1))) A__G(s(s(f(z0)))) -> c3(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) A__G(s(s(g(z0)))) -> c3(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) A__G(s(s(sel(z0, z1)))) -> c3(A__G(s(a__sel(mark(z0), mark(z1)))), MARK(s(sel(z0, z1)))) A__G(s(s(cons(z0, z1)))) -> c3(A__G(s(cons(mark(z0), z1))), MARK(s(cons(z0, z1)))) A__G(s(s(s(z0)))) -> c3(A__G(s(s(mark(z0)))), MARK(s(s(z0)))) A__G(s(s(x0))) -> c3(MARK(s(x0))) A__G(s(s(0))) -> c3(MARK(s(0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c6(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c6(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, f(0))) -> c6(A__SEL(mark(x0), a__f(0)), MARK(x0)) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c6(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c6(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c6(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, f(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, f(x2))) -> c6(A__SEL(0, a__f(mark(x2)))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c6(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c6(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, g(0))) -> c6(A__SEL(mark(x0), a__g(0)), MARK(x0)) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c6(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c6(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c6(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, g(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, g(x2))) -> c6(A__SEL(0, a__g(mark(x2)))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c6(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(f(z0))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(g(z0))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(f(f(z0)))) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(f(g(z0)))) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(f(sel(z0, z1)))) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(f(cons(z0, z1)))) A__SEL(s(f(0)), cons(x1, x2)) -> c6(A__SEL(a__f(0), mark(x2)), MARK(f(0))) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(f(s(z0)))) A__SEL(s(f(x0)), cons(x1, x2)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, 0)) -> c6(MARK(f(x0))) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c6(MARK(f(x0))) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(g(f(z0)))) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(g(g(z0)))) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(g(sel(z0, z1)))) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(g(cons(z0, z1)))) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(g(s(z0)))) A__SEL(s(g(x0)), cons(x1, 0)) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c6(MARK(g(x0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c6(MARK(g(x0))) A__SEL(s(g(0)), cons(x1, x2)) -> c6(A__SEL(a__g(0), mark(x2))) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(sel(x0, f(z0)))) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(sel(x0, g(z0)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(sel(x0, s(z0)))) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(sel(f(z0), x1))) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(sel(g(z0), x1))) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(sel(z0, z1), x1))) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(sel(cons(z0, z1), x1))) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(sel(s(z0), x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(s(f(z0)))) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(s(g(z0)))) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(s(sel(z0, z1)))) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(s(cons(z0, z1)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), f(g(mark(x2))))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(f(z0)))) -> c7(A__SEL(mark(x0), a__f(a__f(mark(z0)))), MARK(f(f(z0)))) A__SEL(s(x0), cons(x1, f(g(z0)))) -> c7(A__SEL(mark(x0), a__f(a__g(mark(z0)))), MARK(f(g(z0)))) A__SEL(s(x0), cons(x1, f(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) A__SEL(s(x0), cons(x1, f(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) A__SEL(s(x0), cons(x1, f(0))) -> c7(A__SEL(mark(x0), a__f(0)), MARK(f(0))) A__SEL(s(x0), cons(x1, f(s(z0)))) -> c7(A__SEL(mark(x0), a__f(s(mark(z0)))), MARK(f(s(z0)))) A__SEL(s(f(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__f(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(g(z0)), cons(x1, f(x2))) -> c7(A__SEL(a__g(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(sel(z0, z1)), cons(x1, f(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(0), cons(x1, f(x2))) -> c7(A__SEL(0, a__f(mark(x2))), MARK(f(x2))) A__SEL(s(s(z0)), cons(x1, f(x2))) -> c7(A__SEL(s(mark(z0)), a__f(mark(x2))), MARK(f(x2))) A__SEL(s(x0), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(cons(z0, z1)), cons(x1, f(x2))) -> c7(MARK(f(x2))) A__SEL(s(x0), cons(x1, g(f(z0)))) -> c7(A__SEL(mark(x0), a__g(a__f(mark(z0)))), MARK(g(f(z0)))) A__SEL(s(x0), cons(x1, g(g(z0)))) -> c7(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) A__SEL(s(x0), cons(x1, g(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) A__SEL(s(x0), cons(x1, g(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) A__SEL(s(x0), cons(x1, g(s(z0)))) -> c7(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) A__SEL(s(f(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__f(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(g(z0)), cons(x1, g(x2))) -> c7(A__SEL(a__g(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(sel(z0, z1)), cons(x1, g(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(0), cons(x1, g(x2))) -> c7(A__SEL(0, a__g(mark(x2))), MARK(g(x2))) A__SEL(s(s(z0)), cons(x1, g(x2))) -> c7(A__SEL(s(mark(z0)), a__g(mark(x2))), MARK(g(x2))) A__SEL(s(x0), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, g(0))) -> c7(A__SEL(mark(x0), a__g(0))) A__SEL(s(cons(z0, z1)), cons(x1, g(x2))) -> c7(MARK(g(x2))) A__SEL(s(x0), cons(x1, sel(x2, f(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__f(mark(z0)))), MARK(sel(x2, f(z0)))) A__SEL(s(x0), cons(x1, sel(x2, g(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__g(mark(z0)))), MARK(sel(x2, g(z0)))) A__SEL(s(x0), cons(x1, sel(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(sel(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), cons(mark(z0), z1))), MARK(sel(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(sel(x2, s(z0)))) A__SEL(s(x0), cons(x1, sel(f(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x3))), MARK(sel(f(z0), x3))) A__SEL(s(x0), cons(x1, sel(g(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x3))), MARK(sel(g(z0), x3))) A__SEL(s(x0), cons(x1, sel(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(sel(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x3))), MARK(sel(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, sel(0, x3))) -> c7(A__SEL(mark(x0), a__sel(0, mark(x3))), MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(g(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(s(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(f(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__f(mark(z0)), x3)), MARK(cons(f(z0), x3))) A__SEL(s(x0), cons(x1, cons(g(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__g(mark(z0)), x3)), MARK(cons(g(z0), x3))) A__SEL(s(x0), cons(x1, cons(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x3)), MARK(cons(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(cons(mark(z0), z1), x3)), MARK(cons(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, cons(0, x3))) -> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), x3))) A__SEL(s(f(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__f(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(g(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__g(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(f(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(f(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__f(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(f(0)), cons(x1, x2)) -> c7(A__SEL(a__f(0), mark(x2)), MARK(x2)) A__SEL(s(f(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__f(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(f(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(f(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(g(f(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(g(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(g(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__g(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(g(0)), cons(x1, x2)) -> c7(A__SEL(a__g(0), mark(x2)), MARK(x2)) A__SEL(s(g(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__g(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(g(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(g(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(sel(x0, f(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__f(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, g(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__g(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(f(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__f(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(g(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__g(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(s(f(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__f(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(g(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__g(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(s(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(s(0)), cons(x1, x2)) -> c7(A__SEL(s(0), mark(x2)), MARK(x2)) A__SEL(s(s(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) MARK(g(f(f(z0)))) -> c10(A__G(a__f(a__f(mark(z0)))), MARK(f(f(z0)))) MARK(g(f(g(z0)))) -> c10(A__G(a__f(a__g(mark(z0)))), MARK(f(g(z0)))) MARK(g(f(sel(z0, z1)))) -> c10(A__G(a__f(a__sel(mark(z0), mark(z1)))), MARK(f(sel(z0, z1)))) MARK(g(f(cons(z0, z1)))) -> c10(A__G(a__f(cons(mark(z0), z1))), MARK(f(cons(z0, z1)))) MARK(g(f(0))) -> c10(A__G(a__f(0)), MARK(f(0))) MARK(g(f(s(z0)))) -> c10(A__G(a__f(s(mark(z0)))), MARK(f(s(z0)))) MARK(g(f(x0))) -> c10(MARK(f(x0))) MARK(g(g(f(z0)))) -> c10(A__G(a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(g(g(g(z0)))) -> c10(A__G(a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(g(g(sel(z0, z1)))) -> c10(A__G(a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(g(g(cons(z0, z1)))) -> c10(A__G(a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(g(g(s(z0)))) -> c10(A__G(a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(g(g(x0))) -> c10(MARK(g(x0))) MARK(g(g(0))) -> c10(A__G(a__g(0))) MARK(g(sel(x0, f(z0)))) -> c10(A__G(a__sel(mark(x0), a__f(mark(z0)))), MARK(sel(x0, f(z0)))) MARK(g(sel(x0, g(z0)))) -> c10(A__G(a__sel(mark(x0), a__g(mark(z0)))), MARK(sel(x0, g(z0)))) MARK(g(sel(x0, sel(z0, z1)))) -> c10(A__G(a__sel(mark(x0), a__sel(mark(z0), mark(z1)))), MARK(sel(x0, sel(z0, z1)))) MARK(g(sel(x0, cons(z0, z1)))) -> c10(A__G(a__sel(mark(x0), cons(mark(z0), z1))), MARK(sel(x0, cons(z0, z1)))) MARK(g(sel(x0, 0))) -> c10(A__G(a__sel(mark(x0), 0)), MARK(sel(x0, 0))) MARK(g(sel(x0, s(z0)))) -> c10(A__G(a__sel(mark(x0), s(mark(z0)))), MARK(sel(x0, s(z0)))) MARK(g(sel(f(z0), x1))) -> c10(A__G(a__sel(a__f(mark(z0)), mark(x1))), MARK(sel(f(z0), x1))) MARK(g(sel(g(z0), x1))) -> c10(A__G(a__sel(a__g(mark(z0)), mark(x1))), MARK(sel(g(z0), x1))) MARK(g(sel(sel(z0, z1), x1))) -> c10(A__G(a__sel(a__sel(mark(z0), mark(z1)), mark(x1))), MARK(sel(sel(z0, z1), x1))) MARK(g(sel(cons(z0, z1), x1))) -> c10(A__G(a__sel(cons(mark(z0), z1), mark(x1))), MARK(sel(cons(z0, z1), x1))) MARK(g(sel(0, x1))) -> c10(A__G(a__sel(0, mark(x1))), MARK(sel(0, x1))) MARK(g(sel(s(z0), x1))) -> c10(A__G(a__sel(s(mark(z0)), mark(x1))), MARK(sel(s(z0), x1))) MARK(g(sel(x0, x1))) -> c10(MARK(sel(x0, x1))) MARK(g(s(f(z0)))) -> c10(A__G(s(a__f(mark(z0)))), MARK(s(f(z0)))) MARK(g(s(g(z0)))) -> c10(A__G(s(a__g(mark(z0)))), MARK(s(g(z0)))) MARK(g(s(sel(z0, z1)))) -> c10(A__G(s(a__sel(mark(z0), mark(z1)))), 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c11(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(g(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c11(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c11(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c11(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(f(z0), sel(x1, x2))) -> c11(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(f(z0))) MARK(sel(g(z0), sel(x1, x2))) -> c11(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(g(z0))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c11(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c11(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) 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a__g(a__f(mark(z0)))), MARK(g(f(z0)))) MARK(sel(x0, g(g(z0)))) -> c12(A__SEL(mark(x0), a__g(a__g(mark(z0)))), MARK(g(g(z0)))) MARK(sel(x0, g(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(a__sel(mark(z0), mark(z1)))), MARK(g(sel(z0, z1)))) MARK(sel(x0, g(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__g(cons(mark(z0), z1))), MARK(g(cons(z0, z1)))) MARK(sel(x0, g(s(z0)))) -> c12(A__SEL(mark(x0), a__g(s(mark(z0)))), MARK(g(s(z0)))) MARK(sel(f(z0), g(x1))) -> c12(A__SEL(a__f(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(g(z0), g(x1))) -> c12(A__SEL(a__g(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(sel(z0, z1), g(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(0, g(x1))) -> c12(A__SEL(0, a__g(mark(x1))), MARK(g(x1))) MARK(sel(s(z0), g(x1))) -> c12(A__SEL(s(mark(z0)), a__g(mark(x1))), MARK(g(x1))) MARK(sel(x0, g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, g(0))) -> c12(A__SEL(mark(x0), a__g(0))) MARK(sel(cons(z0, z1), g(x1))) -> c12(MARK(g(x1))) MARK(sel(x0, sel(x1, f(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__f(mark(z0)))), MARK(sel(x1, f(z0)))) MARK(sel(x0, sel(x1, g(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__g(mark(z0)))), MARK(sel(x1, g(z0)))) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(sel(x0, sel(f(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__f(mark(z0)), mark(x2))), MARK(sel(f(z0), x2))) MARK(sel(x0, sel(g(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__g(mark(z0)), mark(x2))), MARK(sel(g(z0), x2))) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(sel(f(z0), sel(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(g(z0), sel(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(sel(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(sel(x1, x2))) MARK(sel(x0, cons(f(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__f(mark(z0)), x2)), MARK(cons(f(z0), x2))) MARK(sel(x0, cons(g(z0), x2))) -> c12(A__SEL(mark(x0), cons(a__g(mark(z0)), x2)), MARK(cons(g(z0), x2))) MARK(sel(x0, cons(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(sel(x0, cons(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(sel(x0, cons(0, x2))) -> c12(A__SEL(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(sel(x0, cons(s(z0), x2))) -> c12(A__SEL(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(sel(f(z0), cons(x1, x2))) -> c12(A__SEL(a__f(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(g(z0), cons(x1, x2))) -> c12(A__SEL(a__g(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(sel(z0, z1), cons(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(0, cons(x1, x2))) -> c12(A__SEL(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(s(z0), cons(x1, x2))) -> c12(A__SEL(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(sel(x0, cons(x1, x2))) -> c12(MARK(cons(x1, x2))) MARK(sel(cons(z0, z1), cons(x1, x2))) -> c12(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__f_1, a__g_1, a__sel_2, mark_1 Defined Pair Symbols: A__F_1, A__SEL_2, MARK_1, A__G_1 Compound Symbols: c_1, c5_1, c9_2, c13_1, c15_1, c3_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c3_2, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (253) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (254) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) [1] a__g(0) -> s(0) [1] a__g(s(X)) -> s(s(a__g(mark(X)))) [1] a__sel(0, cons(X, Y)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(f(X)) -> a__f(mark(X)) [1] mark(g(X)) -> a__g(mark(X)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__f(X) -> f(X) [1] a__g(X) -> g(X) [1] a__sel(X1, X2) -> sel(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (255) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (256) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) [1] a__g(0) -> s(0) [1] a__g(s(X)) -> s(s(a__g(mark(X)))) [1] a__sel(0, cons(X, Y)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(f(X)) -> a__f(mark(X)) [1] mark(g(X)) -> a__g(mark(X)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__f(X) -> f(X) [1] a__g(X) -> g(X) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel cons :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel mark :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel 0 :: g:f:cons:0:s:sel s :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel Rewrite Strategy: INNERMOST ---------------------------------------- (257) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__g_1 a__sel_2 a__f_1 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (258) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) [1] a__g(0) -> s(0) [1] a__g(s(X)) -> s(s(a__g(mark(X)))) [1] a__sel(0, cons(X, Y)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(f(X)) -> a__f(mark(X)) [1] mark(g(X)) -> a__g(mark(X)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__f(X) -> f(X) [1] a__g(X) -> g(X) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel cons :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel mark :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel 0 :: g:f:cons:0:s:sel s :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel Rewrite Strategy: INNERMOST ---------------------------------------- (259) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (260) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) [1] a__g(0) -> s(0) [1] a__g(s(f(X'))) -> s(s(a__g(a__f(mark(X'))))) [2] a__g(s(g(X''))) -> s(s(a__g(a__g(mark(X''))))) [2] a__g(s(sel(X1', X2'))) -> s(s(a__g(a__sel(mark(X1'), mark(X2'))))) [2] a__g(s(cons(X1'', X2''))) -> s(s(a__g(cons(mark(X1''), X2'')))) [2] a__g(s(0)) -> s(s(a__g(0))) [2] a__g(s(s(X3))) -> s(s(a__g(s(mark(X3))))) [2] a__sel(0, cons(X, Y)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(f(f(X39))) -> a__f(a__f(mark(X39))) [2] mark(f(g(X40))) -> a__f(a__g(mark(X40))) [2] mark(f(sel(X118, X216))) -> a__f(a__sel(mark(X118), mark(X216))) [2] mark(f(cons(X119, X217))) -> a__f(cons(mark(X119), X217)) [2] mark(f(0)) -> a__f(0) [2] mark(f(s(X41))) -> a__f(s(mark(X41))) [2] mark(g(f(X42))) -> a__g(a__f(mark(X42))) [2] mark(g(g(X43))) -> a__g(a__g(mark(X43))) [2] mark(g(sel(X120, X218))) -> a__g(a__sel(mark(X120), mark(X218))) [2] mark(g(cons(X121, X219))) -> a__g(cons(mark(X121), X219)) [2] mark(g(0)) -> a__g(0) [2] mark(g(s(X44))) -> a__g(s(mark(X44))) [2] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__f(X) -> f(X) [1] a__g(X) -> g(X) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel cons :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel mark :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel 0 :: g:f:cons:0:s:sel s :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel Rewrite Strategy: INNERMOST ---------------------------------------- (261) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 ---------------------------------------- (262) Obligation: Complexity RNTS consisting of the following rules: a__f(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__f(z) -{ 1 }-> 1 + mark(X) + (1 + (1 + X)) :|: X >= 0, z = X a__g(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__g(z) -{ 1 }-> 1 + 0 :|: z = 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(a__sel(mark(X1'), mark(X2')))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(a__g(mark(X'')))) :|: z = 1 + (1 + X''), X'' >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(a__f(mark(X')))) :|: X' >= 0, z = 1 + (1 + X') a__g(z) -{ 2 }-> 1 + (1 + a__g(0)) :|: z = 1 + 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(1 + mark(X3))) :|: z = 1 + (1 + X3), X3 >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(1 + mark(X1'') + X2'')) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 a__sel(z, z') -{ 1 }-> mark(X) :|: Y >= 0, X >= 0, z' = 1 + X + Y, z = 0 a__sel(z, z') -{ 1 }-> a__sel(mark(X), mark(Z)) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__sel(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__sel(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__g(a__sel(mark(X120), mark(X218))) :|: X120 >= 0, z = 1 + (1 + X120 + X218), X218 >= 0 mark(z) -{ 2 }-> a__g(a__g(mark(X43))) :|: X43 >= 0, z = 1 + (1 + X43) mark(z) -{ 2 }-> a__g(a__f(mark(X42))) :|: X42 >= 0, z = 1 + (1 + X42) mark(z) -{ 2 }-> a__g(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__g(1 + mark(X44)) :|: z = 1 + (1 + X44), X44 >= 0 mark(z) -{ 2 }-> a__g(1 + mark(X121) + X219) :|: X219 >= 0, z = 1 + (1 + X121 + X219), X121 >= 0 mark(z) -{ 2 }-> a__f(a__sel(mark(X118), mark(X216))) :|: X118 >= 0, X216 >= 0, z = 1 + (1 + X118 + X216) mark(z) -{ 2 }-> a__f(a__g(mark(X40))) :|: z = 1 + (1 + X40), X40 >= 0 mark(z) -{ 2 }-> a__f(a__f(mark(X39))) :|: z = 1 + (1 + X39), X39 >= 0 mark(z) -{ 2 }-> a__f(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__f(1 + mark(X41)) :|: X41 >= 0, z = 1 + (1 + X41) mark(z) -{ 2 }-> a__f(1 + mark(X119) + X217) :|: z = 1 + (1 + X119 + X217), X119 >= 0, X217 >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (263) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (264) Obligation: Complexity RNTS consisting of the following rules: a__f(z) -{ 1 }-> 1 + z :|: z >= 0 a__f(z) -{ 1 }-> 1 + mark(z) + (1 + (1 + z)) :|: z >= 0 a__g(z) -{ 1 }-> 1 + z :|: z >= 0 a__g(z) -{ 1 }-> 1 + 0 :|: z = 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(a__sel(mark(X1'), mark(X2')))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(a__g(mark(z - 2)))) :|: z - 2 >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(a__f(mark(z - 2)))) :|: z - 2 >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(0)) :|: z = 1 + 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(1 + mark(z - 2))) :|: z - 2 >= 0 a__g(z) -{ 2 }-> 1 + (1 + a__g(1 + mark(X1'') + X2'')) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 a__sel(z, z') -{ 1 }-> mark(X) :|: Y >= 0, X >= 0, z' = 1 + X + Y, z = 0 a__sel(z, z') -{ 1 }-> a__sel(mark(z - 1), mark(Z)) :|: Z >= 0, Y >= 0, z - 1 >= 0, z' = 1 + Y + Z a__sel(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__sel(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__g(a__sel(mark(X120), mark(X218))) :|: X120 >= 0, z = 1 + (1 + X120 + X218), X218 >= 0 mark(z) -{ 2 }-> a__g(a__g(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__g(a__f(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__g(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__g(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__g(1 + mark(X121) + X219) :|: X219 >= 0, z = 1 + (1 + X121 + X219), X121 >= 0 mark(z) -{ 2 }-> a__f(a__sel(mark(X118), mark(X216))) :|: X118 >= 0, X216 >= 0, z = 1 + (1 + X118 + X216) mark(z) -{ 2 }-> a__f(a__g(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__f(a__f(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__f(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__f(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__f(1 + mark(X119) + X217) :|: z = 1 + (1 + X119 + X217), X119 >= 0, X217 >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (265) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (266) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__f(X) -> cons(mark(X), f(g(X))) [1] a__g(0) -> s(0) [1] a__g(s(X)) -> s(s(a__g(mark(X)))) [1] a__sel(0, cons(X, Y)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(f(X)) -> a__f(mark(X)) [1] mark(g(X)) -> a__g(mark(X)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] a__f(X) -> f(X) [1] a__g(X) -> g(X) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel cons :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel mark :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel f :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__g :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel 0 :: g:f:cons:0:s:sel s :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel a__sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel sel :: g:f:cons:0:s:sel -> g:f:cons:0:s:sel -> g:f:cons:0:s:sel Rewrite Strategy: INNERMOST ---------------------------------------- (267) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 ---------------------------------------- (268) Obligation: Complexity RNTS consisting of the following rules: a__f(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__f(z) -{ 1 }-> 1 + mark(X) + (1 + (1 + X)) :|: X >= 0, z = X a__g(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__g(z) -{ 1 }-> 1 + 0 :|: z = 0 a__g(z) -{ 1 }-> 1 + (1 + a__g(mark(X))) :|: z = 1 + X, X >= 0 a__sel(z, z') -{ 1 }-> mark(X) :|: Y >= 0, X >= 0, z' = 1 + X + Y, z = 0 a__sel(z, z') -{ 1 }-> a__sel(mark(X), mark(Z)) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__sel(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__sel(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__g(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__f(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> 1 + mark(X1) + X2 :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity.