KILLED proof of input_JRnqJtcrZG.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CompletionProof [UPPER BOUND(ID), 0 ms] (18) CpxTypedWeightedCompleteTrs (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (22) CdtProblem (23) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 7 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (66) CdtProblem (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [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), 1 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 127 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 60 ms] (122) CdtProblem (123) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 76 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 112 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 93 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 26 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 89 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 126 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 120 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 159 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 142 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 123 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 32 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 102 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 141 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 64 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 68 ms] (204) CdtProblem (205) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 101 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 197 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 141 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 17 ms] (222) CdtProblem ---------------------------------------- (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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) 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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) 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 ---------------------------------------- (9) 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 ---------------------------------------- (10) 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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) 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 ---------------------------------------- (13) 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 ---------------------------------------- (14) 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 ---------------------------------------- (15) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (16) 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 ---------------------------------------- (17) 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 ---------------------------------------- (18) 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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. ---------------------------------------- (21) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (22) 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 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing nodes: A__SEL(z0, z1) -> c8 A__G(0) -> c2 A__F(z0) -> c1 MARK(0) -> c14 A__G(z0) -> c4 ---------------------------------------- (24) 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 ---------------------------------------- (25) 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))) ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__G(s(0)) -> c3(A__G(0), MARK(0)) ---------------------------------------- (28) 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 ---------------------------------------- (29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (30) 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 ---------------------------------------- (31) 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))) ---------------------------------------- (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__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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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__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 ---------------------------------------- (35) 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)) ---------------------------------------- (36) 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 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) ---------------------------------------- (38) 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 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (40) 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 ---------------------------------------- (41) 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))) ---------------------------------------- (42) 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 ---------------------------------------- (43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(g(0)) -> c10(A__G(0), MARK(0)) ---------------------------------------- (44) 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 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (46) 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 ---------------------------------------- (47) 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))) ---------------------------------------- (48) 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 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (50) 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 ---------------------------------------- (51) 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)) ---------------------------------------- (52) 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 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(0)) ---------------------------------------- (54) 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 ---------------------------------------- (55) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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)) 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 ---------------------------------------- (57) 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))) ---------------------------------------- (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)) 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 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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)) 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 ---------------------------------------- (61) 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)))) ---------------------------------------- (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)) 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 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 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)) 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 ---------------------------------------- (65) 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))) ---------------------------------------- (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(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 ---------------------------------------- (67) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (69) 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))) ---------------------------------------- (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(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 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (73) 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))) ---------------------------------------- (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(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 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (77) 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))) ---------------------------------------- (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(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)))) -> 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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))) -> 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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 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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(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)))) 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(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 ---------------------------------------- (81) 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))) ---------------------------------------- (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(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))) -> 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))) 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 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (85) 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))) ---------------------------------------- (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(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)))) -> 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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, 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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 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (89) 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))) ---------------------------------------- (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(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))) 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 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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(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, 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))) 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 ---------------------------------------- (93) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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))) -> 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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)), 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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 ---------------------------------------- (97) 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))) ---------------------------------------- (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(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 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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), 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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)), 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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 ---------------------------------------- (101) 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))) ---------------------------------------- (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, 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))) 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 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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))), 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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 ---------------------------------------- (105) 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)))) ---------------------------------------- (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, 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 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(0), cons(x0, s(z0))) -> c6(A__SEL(0, s(mark(z0)))) A__SEL(s(0), cons(x0, 0)) -> c6(A__SEL(0, 0)) ---------------------------------------- (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, 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 ---------------------------------------- (109) 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))) ---------------------------------------- (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, 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))) 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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 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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))) -> 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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 ---------------------------------------- (113) 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))) ---------------------------------------- (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, 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), 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))) 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 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (117) 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))) ---------------------------------------- (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(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))) 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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, 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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), 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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)), 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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(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 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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))) 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 ---------------------------------------- (121) 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))) ---------------------------------------- (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(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), 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-> 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 ---------------------------------------- (123) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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(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))), 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))) 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 ---------------------------------------- (125) 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)) ---------------------------------------- (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(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)))), 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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, 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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)) -> 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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 ---------------------------------------- (127) 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)) ---------------------------------------- (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(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, 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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))) -> 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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 ---------------------------------------- (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(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(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, 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)) 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 ---------------------------------------- (131) 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)) ---------------------------------------- (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(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, 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)) 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, 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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)) -> 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, 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 ---------------------------------------- (133) 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)) ---------------------------------------- (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(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)), 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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 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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), 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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)) -> 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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) -> 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)) 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) 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)) ---------------------------------------- (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(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), 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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 ---------------------------------------- (139) 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)) ---------------------------------------- (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(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 ---------------------------------------- (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(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 ---------------------------------------- (143) 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))) ---------------------------------------- (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(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))) -> 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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)) -> 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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)), 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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))), 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 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) ---------------------------------------- (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(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 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)) 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))) 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) 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)) ---------------------------------------- (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, 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), 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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))), 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 ---------------------------------------- (151) 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)) ---------------------------------------- (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(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 ---------------------------------------- (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(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), 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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, 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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), 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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 ---------------------------------------- (155) 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))) ---------------------------------------- (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(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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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))) 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)), 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(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 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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, 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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)), 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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, 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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)) -> 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))) 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))) -> 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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))) 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 ---------------------------------------- (159) 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)))) ---------------------------------------- (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(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, 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)))) 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), 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(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 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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, 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), 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))) 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 ---------------------------------------- (163) 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))) ---------------------------------------- (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(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)) 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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 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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, 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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))) 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, 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 ---------------------------------------- (167) 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))) ---------------------------------------- (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(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)) 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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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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))) 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 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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, 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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))) 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)), 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 ---------------------------------------- (171) 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))) ---------------------------------------- (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(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)))) -> 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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(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))) 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 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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), 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)))) 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 ---------------------------------------- (175) 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))) ---------------------------------------- (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(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), 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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)), 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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 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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)) -> 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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 ---------------------------------------- (179) 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))) ---------------------------------------- (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(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, 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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)))) -> 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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 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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)))) -> 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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)))) -> 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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), 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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)))) 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, 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), 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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))), 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 ---------------------------------------- (183) 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))) ---------------------------------------- (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(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(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))) 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, 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(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 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)))) -> 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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))) 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, 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))) 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 ---------------------------------------- (187) 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))) ---------------------------------------- (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(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))) 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-> 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, 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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 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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, 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))) 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 ---------------------------------------- (191) 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)))) ---------------------------------------- (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(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))), 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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(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 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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(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))) 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)))) -> 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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 ---------------------------------------- (195) 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))) ---------------------------------------- (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(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), 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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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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)))) -> 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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 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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, 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)))) -> 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))) 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) 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))) ---------------------------------------- (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, 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)), 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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))) 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(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 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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))), 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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)) -> 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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 ---------------------------------------- (203) 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)))) ---------------------------------------- (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, 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), 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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 ---------------------------------------- (205) 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)) ---------------------------------------- (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, 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), 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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)), 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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))) 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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)))) -> 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 ---------------------------------------- (207) 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))) ---------------------------------------- (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, 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))) 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(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))) 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), 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), 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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)) -> 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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 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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, 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)), 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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)) 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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))) 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), 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)) -> 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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 ---------------------------------------- (211) 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))) ---------------------------------------- (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, 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)) 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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)))) 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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)) 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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 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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, 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))) 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 ---------------------------------------- (215) 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))) ---------------------------------------- (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(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), 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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))) -> 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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))) 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)) -> 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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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)), 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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)), 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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 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (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(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)), 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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, 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)) -> 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))) 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 ---------------------------------------- (219) 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))) ---------------------------------------- (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(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), 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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)) -> 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-> 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(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))) 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, 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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 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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)))), 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)))), 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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)))), 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)) -> 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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