KILLED proof of input_LOExWCmMrO.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF).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), 31 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), 1 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (50) CdtProblem (51) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 31 ms] (74) CdtProblem (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms] (80) CdtProblem (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 48 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 63 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 12 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 44 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 163 ms] (114) CdtProblem (115) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 123 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 125 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 127 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 15 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 33 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 163 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 34 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 44 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 119 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 94 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 26 ms] (158) CdtProblem (159) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (170) CdtProblem (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 52 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 169 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 43 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 72 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 96 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 81 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 144 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 126 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 23 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 206 ms] (208) CdtProblem (209) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 64 ms] (210) CdtProblem (211) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 79 ms] (212) CdtProblem (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 229 ms] (214) CdtProblem (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 55 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 79 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 200 ms] (220) CdtProblem (221) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 20 ms] (222) CdtProblem (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 70 ms] (224) CdtProblem (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 143 ms] (226) CdtProblem (227) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 19 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 275 ms] (232) CdtProblem (233) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 33 ms] (234) CdtProblem (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 101 ms] (236) CdtProblem (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 384 ms] (238) CdtProblem (239) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 99 ms] (240) CdtProblem (241) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 72 ms] (242) CdtProblem (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 504 ms] (244) CdtProblem (245) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 131 ms] (246) CdtProblem (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 114 ms] (248) 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__from(X) -> cons(mark(X), from(s(X))) a__first(0, Z) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__sel(0, cons(X, Z)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(from(X)) -> a__from(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(nil) -> nil a__from(X) -> from(X) a__first(X1, X2) -> first(X1, X2) 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__from(X) -> cons(mark(X), from(s(X))) a__first(0', Z) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__sel(0', cons(X, Z)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(from(X)) -> a__from(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0') -> 0' mark(nil) -> nil a__from(X) -> from(X) a__first(X1, X2) -> first(X1, X2) 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__from(X) -> cons(mark(X), from(s(X))) a__first(0, Z) -> nil a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) a__sel(0, cons(X, Z)) -> mark(X) a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) mark(from(X)) -> a__from(mark(X)) mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 mark(nil) -> nil a__from(X) -> from(X) a__first(X1, X2) -> first(X1, X2) 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__from(X) -> cons(mark(X), from(s(X))) [1] a__first(0, Z) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__sel(0, cons(X, Z)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__from(X) -> from(X) [1] a__first(X1, X2) -> first(X1, X2) [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__from(X) -> cons(mark(X), from(s(X))) [1] a__first(0, Z) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__sel(0, cons(X, Z)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__from(X) -> from(X) [1] a__first(X1, X2) -> first(X1, X2) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel cons :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel mark :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel s :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel 0 :: s:from:cons:0:nil:first:sel nil :: s:from:cons:0:nil:first:sel first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first: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__sel_2 a__from_1 a__first_2 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__from(X) -> cons(mark(X), from(s(X))) [1] a__first(0, Z) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__sel(0, cons(X, Z)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__from(X) -> from(X) [1] a__first(X1, X2) -> first(X1, X2) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel cons :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel mark :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel s :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel 0 :: s:from:cons:0:nil:first:sel nil :: s:from:cons:0:nil:first:sel first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first: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__from(X) -> cons(mark(X), from(s(X))) [1] a__first(0, Z) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__sel(0, cons(X, Z)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(from(from(X35))) -> a__from(a__from(mark(X35))) [2] mark(from(first(X123, X223))) -> a__from(a__first(mark(X123), mark(X223))) [2] mark(from(sel(X124, X224))) -> a__from(a__sel(mark(X124), mark(X224))) [2] mark(from(cons(X125, X225))) -> a__from(cons(mark(X125), X225)) [2] mark(from(s(X36))) -> a__from(s(mark(X36))) [2] mark(from(0)) -> a__from(0) [2] mark(from(nil)) -> a__from(nil) [2] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__from(X) -> from(X) [1] a__first(X1, X2) -> first(X1, X2) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel cons :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel mark :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel s :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel 0 :: s:from:cons:0:nil:first:sel nil :: s:from:cons:0:nil:first:sel first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first: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 nil => 1 ---------------------------------------- (14) Obligation: Complexity RNTS consisting of the following rules: a__first(z, z') -{ 1 }-> 1 :|: Z >= 0, z' = Z, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__from(z) -{ 1 }-> 1 + mark(X) + (1 + (1 + X)) :|: X >= 0, z = X a__sel(z, z') -{ 1 }-> mark(X) :|: Z >= 0, X >= 0, z = 0, z' = 1 + X + Z 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__from(a__sel(mark(X124), mark(X224))) :|: X124 >= 0, X224 >= 0, z = 1 + (1 + X124 + X224) mark(z) -{ 2 }-> a__from(a__from(mark(X35))) :|: z = 1 + (1 + X35), X35 >= 0 mark(z) -{ 2 }-> a__from(a__first(mark(X123), mark(X223))) :|: X223 >= 0, z = 1 + (1 + X123 + X223), X123 >= 0 mark(z) -{ 2 }-> a__from(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__from(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__from(1 + mark(X36)) :|: X36 >= 0, z = 1 + (1 + X36) mark(z) -{ 2 }-> a__from(1 + mark(X125) + X225) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 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__first(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0 a__first(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + (z - 1) + Z) :|: Z >= 0, Y >= 0, z - 1 >= 0, z' = 1 + Y + Z a__from(z) -{ 1 }-> 1 + z :|: z >= 0 a__from(z) -{ 1 }-> 1 + mark(z) + (1 + (1 + z)) :|: z >= 0 a__sel(z, z') -{ 1 }-> mark(X) :|: Z >= 0, X >= 0, z = 0, z' = 1 + X + Z 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__from(a__sel(mark(X124), mark(X224))) :|: X124 >= 0, X224 >= 0, z = 1 + (1 + X124 + X224) mark(z) -{ 2 }-> a__from(a__from(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__from(a__first(mark(X123), mark(X223))) :|: X223 >= 0, z = 1 + (1 + X123 + X223), X123 >= 0 mark(z) -{ 2 }-> a__from(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__from(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__from(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__from(1 + mark(X125) + X225) :|: X125 >= 0, X225 >= 0, z = 1 + (1 + X125 + X225) mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 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__from(X) -> cons(mark(X), from(s(X))) [1] a__first(0, Z) -> nil [1] a__first(s(X), cons(Y, Z)) -> cons(mark(Y), first(X, Z)) [1] a__sel(0, cons(X, Z)) -> mark(X) [1] a__sel(s(X), cons(Y, Z)) -> a__sel(mark(X), mark(Z)) [1] mark(from(X)) -> a__from(mark(X)) [1] mark(first(X1, X2)) -> a__first(mark(X1), mark(X2)) [1] mark(sel(X1, X2)) -> a__sel(mark(X1), mark(X2)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] mark(nil) -> nil [1] a__from(X) -> from(X) [1] a__first(X1, X2) -> first(X1, X2) [1] a__sel(X1, X2) -> sel(X1, X2) [1] The TRS has the following type information: a__from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel cons :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel mark :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel from :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel s :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel 0 :: s:from:cons:0:nil:first:sel nil :: s:from:cons:0:nil:first:sel first :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel a__sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel sel :: s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first:sel -> s:from:cons:0:nil:first: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 nil => 1 ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: a__first(z, z') -{ 1 }-> 1 :|: Z >= 0, z' = Z, z = 0 a__first(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__first(z, z') -{ 1 }-> 1 + mark(Y) + (1 + X + Z) :|: Z >= 0, z = 1 + X, Y >= 0, X >= 0, z' = 1 + Y + Z a__from(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__from(z) -{ 1 }-> 1 + mark(X) + (1 + (1 + X)) :|: X >= 0, z = X a__sel(z, z') -{ 1 }-> mark(X) :|: Z >= 0, X >= 0, z = 0, z' = 1 + X + Z 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__from(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__first(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 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__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1 A__FIRST(0, z0) -> c2 A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__FIRST(z0, z1) -> 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(nil) -> c17 S tuples: A__FROM(z0) -> c(MARK(z0)) A__FROM(z0) -> c1 A__FIRST(0, z0) -> c2 A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__FIRST(z0, z1) -> 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) MARK(0) -> c16 MARK(nil) -> c17 K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c1, c2, c3_1, c4, c5_1, c6_2, c7_2, c8, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c16, c17 ---------------------------------------- (23) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: A__SEL(z0, z1) -> c8 A__FIRST(0, z0) -> c2 A__FROM(z0) -> c1 MARK(0) -> c16 A__FIRST(z0, z1) -> c4 MARK(nil) -> c17 ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c6_2, c7_2, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1 ---------------------------------------- (25) 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, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(A__SEL(mark(x0), nil), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), 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(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) A__SEL(s(nil), cons(x1, x2)) -> c6(A__SEL(nil, mark(x2)), MARK(nil)) ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(A__SEL(mark(x0), nil), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), 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(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) A__SEL(s(nil), cons(x1, x2)) -> c6(A__SEL(nil, mark(x2)), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(A__SEL(mark(x0), nil), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), 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(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) A__SEL(s(nil), cons(x1, x2)) -> c6(A__SEL(nil, mark(x2)), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c7_2, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2 ---------------------------------------- (27) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(nil), cons(x1, x2)) -> c6(A__SEL(nil, mark(x2)), MARK(nil)) ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(A__SEL(mark(x0), nil), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), 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(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))) -> c6(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(A__SEL(mark(x0), 0), MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(A__SEL(mark(x0), nil), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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(cons(z0, z1)), cons(x1, x2)) -> c6(A__SEL(cons(mark(z0), z1), mark(x2)), 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(0), cons(x1, x2)) -> c6(A__SEL(0, mark(x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c7_2, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2 ---------------------------------------- (29) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) 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(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c7_2, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1 ---------------------------------------- (31) 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) A__SEL(s(x0), cons(x1, nil)) -> c7(A__SEL(mark(x0), nil), MARK(nil)) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(A__SEL(nil, mark(x2)), MARK(x2)) ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) A__SEL(s(x0), cons(x1, nil)) -> c7(A__SEL(mark(x0), nil), MARK(nil)) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(A__SEL(nil, mark(x2)), MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) A__SEL(s(x0), cons(x1, nil)) -> c7(A__SEL(mark(x0), nil), MARK(nil)) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(A__SEL(nil, mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2 ---------------------------------------- (33) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(x0), cons(x1, nil)) -> c7(A__SEL(mark(x0), nil), MARK(nil)) A__SEL(s(x0), cons(x1, 0)) -> c7(A__SEL(mark(x0), 0), MARK(0)) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(A__SEL(nil, mark(x2)), MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(x0), cons(x1, s(z0))) -> c7(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, mark(x2)), MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(A__SEL(nil, mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2 ---------------------------------------- (35) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c10_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1 ---------------------------------------- (37) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c10(A__FIRST(mark(z0), mark(z1)), MARK(z0)) by MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, s(z0))) -> c10(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c10(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c10(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c10(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c10(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c10(A__FIRST(nil, mark(x1)), MARK(nil)) ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, s(z0))) -> c10(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c10(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c10(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c10(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c10(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c10(A__FIRST(nil, mark(x1)), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, s(z0))) -> c10(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c10(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c10(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c10(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(0, x1)) -> c10(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c10(A__FIRST(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, x1)) -> c10(A__FIRST(0, mark(x1)), MARK(0)) MARK(first(nil, x1)) -> c10(A__FIRST(nil, mark(x1)), MARK(nil)) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, s(z0))) -> c10(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c10(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c10(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c10(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(x0, s(z0))) -> c10(A__FIRST(mark(x0), s(mark(z0))), MARK(x0)) MARK(first(x0, 0)) -> c10(A__FIRST(mark(x0), 0), MARK(x0)) MARK(first(x0, nil)) -> c10(A__FIRST(mark(x0), nil), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), x1)) -> c10(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c11_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(z0, z1)) -> c11(A__FIRST(mark(z0), mark(z1)), MARK(z1)) by MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c11(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c11(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c11(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c11(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c11(A__FIRST(nil, mark(x1)), MARK(x1)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c11(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c11(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c11(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c11(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c11(A__FIRST(nil, mark(x1)), MARK(x1)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(x0, 0)) -> c11(A__FIRST(mark(x0), 0), MARK(0)) MARK(first(x0, nil)) -> c11(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c11(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c11(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c11(A__FIRST(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2 ---------------------------------------- (45) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(x0, nil)) -> c11(A__FIRST(mark(x0), nil), MARK(nil)) MARK(first(x0, 0)) -> c11(A__FIRST(mark(x0), 0), MARK(0)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c11(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c11(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c11(A__FIRST(nil, mark(x1)), MARK(x1)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(A__FIRST(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(cons(z0, z1), x1)) -> c11(A__FIRST(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(0, x1)) -> c11(A__FIRST(0, mark(x1)), MARK(x1)) MARK(first(nil, x1)) -> c11(A__FIRST(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c12_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(z0, z1)) -> c12(A__SEL(mark(z0), mark(z1)), MARK(z0)) by MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, nil)) -> c12(A__SEL(mark(x0), nil), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(0)) MARK(sel(nil, x1)) -> c12(A__SEL(nil, mark(x1)), MARK(nil)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, nil)) -> c12(A__SEL(mark(x0), nil), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(0)) MARK(sel(nil, x1)) -> c12(A__SEL(nil, mark(x1)), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, nil)) -> c12(A__SEL(mark(x0), nil), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(0)) MARK(sel(nil, x1)) -> c12(A__SEL(nil, mark(x1)), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2 ---------------------------------------- (51) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(sel(nil, x1)) -> c12(A__SEL(nil, mark(x1)), MARK(nil)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, nil)) -> c12(A__SEL(mark(x0), nil), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(x0, s(z0))) -> c12(A__SEL(mark(x0), s(mark(z0))), MARK(x0)) MARK(sel(x0, 0)) -> c12(A__SEL(mark(x0), 0), MARK(x0)) MARK(sel(x0, nil)) -> c12(A__SEL(mark(x0), nil), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), x1)) -> c12(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c13_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(z0, z1)) -> c13(A__SEL(mark(z0), mark(z1)), MARK(z1)) by MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c13(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(x0, 0)) -> c13(A__SEL(mark(x0), 0), MARK(0)) MARK(sel(x0, nil)) -> c13(A__SEL(mark(x0), nil), MARK(nil)) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c13(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(nil, x1)) -> c13(A__SEL(nil, mark(x1)), MARK(x1)) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c13(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(x0, 0)) -> c13(A__SEL(mark(x0), 0), MARK(0)) MARK(sel(x0, nil)) -> c13(A__SEL(mark(x0), nil), MARK(nil)) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c13(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(nil, x1)) -> c13(A__SEL(nil, mark(x1)), MARK(x1)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c13(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(x0, 0)) -> c13(A__SEL(mark(x0), 0), MARK(0)) MARK(sel(x0, nil)) -> c13(A__SEL(mark(x0), nil), MARK(nil)) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c13(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(nil, x1)) -> c13(A__SEL(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(sel(x0, nil)) -> c13(A__SEL(mark(x0), nil), MARK(nil)) MARK(sel(x0, 0)) -> c13(A__SEL(mark(x0), 0), MARK(0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c13(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c13(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(nil, x1)) -> c13(A__SEL(nil, mark(x1)), MARK(x1)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(x0, s(z0))) -> c13(A__SEL(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(cons(z0, z1), x1)) -> c13(A__SEL(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(nil, x1)) -> c13(A__SEL(nil, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, from(z0))) -> c6(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) by A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), from(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2))), MARK(0)) A__SEL(s(nil), cons(x1, from(x2))) -> c6(A__SEL(nil, a__from(mark(x2))), MARK(nil)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), from(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2))), MARK(0)) A__SEL(s(nil), cons(x1, from(x2))) -> c6(A__SEL(nil, a__from(mark(x2))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), from(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2))), MARK(0)) A__SEL(s(nil), cons(x1, from(x2))) -> c6(A__SEL(nil, a__from(mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (63) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(nil), cons(x1, from(x2))) -> c6(A__SEL(nil, a__from(mark(x2))), MARK(nil)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), from(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2))), MARK(0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), from(mark(x2))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, first(z0, z1))) -> c6(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(0)) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c6(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(nil)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(0)) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c6(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(0)) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c6(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(nil), cons(x1, first(x2, x3))) -> c6(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(nil)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(cons(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (73) 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, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(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(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c6(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(nil)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) 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x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(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(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c6(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) 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, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(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(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c6(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c6(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(nil)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) 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, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(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(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) 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, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(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(0), cons(x1, sel(x2, x3))) -> c6(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, cons(z0, z1))) -> c6(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (79) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) A__SEL(s(nil), cons(x1, cons(x2, x3))) -> c6(A__SEL(nil, cons(mark(x2), x3)), MARK(nil)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) A__SEL(s(nil), cons(x1, cons(x2, x3))) -> c6(A__SEL(nil, cons(mark(x2), x3)), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) A__SEL(s(nil), cons(x1, cons(x2, x3))) -> c6(A__SEL(nil, cons(mark(x2), x3)), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__SEL(s(nil), cons(x1, cons(x2, x3))) -> c6(A__SEL(nil, cons(mark(x2), x3)), MARK(nil)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(s(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(s(mark(z0)), cons(mark(x2), x3)), MARK(s(z0))) A__SEL(s(0), cons(x1, cons(x2, x3))) -> c6(A__SEL(0, cons(mark(x2), x3)), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (83) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), 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mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(from(z0)), cons(x1, x2)) -> c6(A__SEL(a__from(mark(z0)), mark(x2)), MARK(from(z0))) by A__SEL(s(from(x0)), cons(x1, from(z0))) -> c6(A__SEL(a__from(mark(x0)), a__from(mark(z0))), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, first(z0, z1))) -> c6(A__SEL(a__from(mark(x0)), a__first(mark(z0), mark(z1))), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, sel(z0, z1))) -> c6(A__SEL(a__from(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, cons(z0, z1))) -> c6(A__SEL(a__from(mark(x0)), cons(mark(z0), z1)), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(A__SEL(a__from(mark(x0)), 0), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(A__SEL(a__from(mark(x0)), nil), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(A__SEL(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x2)), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(A__SEL(from(mark(x0)), mark(x2)), MARK(from(x0))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), 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A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(x0)), cons(x1, s(z0))) -> c6(A__SEL(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(A__SEL(a__from(mark(x0)), 0), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(A__SEL(a__from(mark(x0)), nil), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(A__SEL(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x2)), MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(A__SEL(from(mark(x0)), mark(x2)), MARK(from(x0))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c6(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(first(z0, z1))) by A__SEL(s(first(x0, x1)), cons(x2, from(z0))) -> c6(A__SEL(a__first(mark(x0), mark(x1)), a__from(mark(z0))), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, first(z0, z1))) -> c6(A__SEL(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, sel(z0, z1))) -> c6(A__SEL(a__first(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, cons(z0, z1))) -> c6(A__SEL(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(A__SEL(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(A__SEL(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(first(x0, x1))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), 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mark(z1)), 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(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(A__SEL(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(A__SEL(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(first(x0, x1))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (93) 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, from(z0))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), a__from(mark(z0))), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, first(z0, z1))) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), 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, 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, 0)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), nil), 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, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) 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cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(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, 0)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), nil), 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, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(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, 0)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(A__SEL(a__sel(mark(x0), mark(x1)), nil), 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, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> 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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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) 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, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_2, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1 ---------------------------------------- (97) 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, from(z0))) -> c6(A__SEL(s(mark(x0)), a__from(mark(z0))), MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, first(z0, z1))) -> c6(A__SEL(s(mark(x0)), a__first(mark(z0), mark(z1))), 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, s(z0))) -> c6(A__SEL(s(mark(x0)), s(mark(z0))), 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, nil)) -> c6(A__SEL(s(mark(x0)), nil), MARK(s(x0))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), 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A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> 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, s(z0))) -> c6(A__SEL(s(mark(x0)), s(mark(z0))), 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, nil)) -> c6(A__SEL(s(mark(x0)), nil), MARK(s(x0))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> 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, s(z0))) -> c6(A__SEL(s(mark(x0)), s(mark(z0))), 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, nil)) -> c6(A__SEL(s(mark(x0)), nil), MARK(s(x0))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), 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MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (101) 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, from(z0))) -> c6(A__SEL(0, a__from(mark(z0)))) A__SEL(s(0), cons(x0, first(z0, z1))) -> c6(A__SEL(0, a__first(mark(z0), mark(z1)))) 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, s(z0))) -> c6(A__SEL(0, s(mark(z0)))) A__SEL(s(0), cons(x0, 0)) -> c6(A__SEL(0, 0)) A__SEL(s(0), cons(x0, nil)) -> c6(A__SEL(0, nil)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) 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)) A__SEL(s(0), cons(x0, nil)) -> c6(A__SEL(0, nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) 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)) A__SEL(s(0), cons(x0, nil)) -> c6(A__SEL(0, nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing nodes: A__SEL(s(0), cons(x0, nil)) -> c6(A__SEL(0, nil)) 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)))) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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, 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c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, from(z0))) -> c7(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) by A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(A__SEL(nil, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), 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x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(A__SEL(nil, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(cons(mark(z0), z1), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(A__SEL(nil, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> 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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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(x0), cons(x1, first(z0, z1))) -> c7(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(A__SEL(mark(x0), first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(cons(mark(z0), z1), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(A__SEL(nil, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (113) 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, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c7(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), 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x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) 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, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c7(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) 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c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) 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, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c7(A__SEL(nil, a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (115) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) 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A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), 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mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), 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cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (117) 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(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(nil), cons(x1, cons(x2, x3))) -> c7(A__SEL(nil, cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(x0), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> 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A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) 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c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(nil), cons(x1, cons(x2, x3))) -> c7(A__SEL(nil, 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__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) 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mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(nil), cons(x1, cons(x2, x3))) -> c7(A__SEL(nil, 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), 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cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), 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c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), 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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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(from(z0)), cons(x1, x2)) -> c7(A__SEL(a__from(mark(z0)), mark(x2)), MARK(x2)) by A__SEL(s(from(x0)), cons(x1, from(z0))) -> c7(A__SEL(a__from(mark(x0)), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(from(x0)), cons(x1, first(z0, z1))) -> c7(A__SEL(a__from(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SEL(s(from(x0)), cons(x1, sel(z0, z1))) -> c7(A__SEL(a__from(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(from(x0)), cons(x1, cons(z0, z1))) -> c7(A__SEL(a__from(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c7(A__SEL(a__from(mark(x0)), 0), MARK(0)) A__SEL(s(from(x0)), cons(x1, nil)) -> c7(A__SEL(a__from(mark(x0)), nil), MARK(nil)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(from(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), 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c7(A__SEL(a__sel(mark(z0), mark(z1)), 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(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c7(A__SEL(a__from(mark(x0)), 0), MARK(0)) A__SEL(s(from(x0)), cons(x1, nil)) -> c7(A__SEL(a__from(mark(x0)), nil), MARK(nil)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(from(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, 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MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), 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cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c7(A__SEL(a__from(mark(x0)), 0), MARK(0)) A__SEL(s(from(x0)), cons(x1, nil)) -> c7(A__SEL(a__from(mark(x0)), nil), MARK(nil)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(from(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (123) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(from(x0)), cons(x1, nil)) -> c7(A__SEL(a__from(mark(x0)), nil), MARK(nil)) A__SEL(s(from(x0)), cons(x1, 0)) -> c7(A__SEL(a__from(mark(x0)), 0), MARK(0)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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, 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c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, 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cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(A__SEL(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(A__SEL(from(mark(x0)), mark(x2)), MARK(x2)) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> 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MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), 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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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c6(MARK(cons(z0, z1))) A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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)), 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from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__SEL(s(first(z0, z1)), cons(x1, x2)) -> c7(A__SEL(a__first(mark(z0), mark(z1)), mark(x2)), MARK(x2)) by A__SEL(s(first(x0, x1)), cons(x2, from(z0))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(first(x0, x1)), cons(x2, first(z0, z1))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) A__SEL(s(first(x0, x1)), cons(x2, sel(z0, z1))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) A__SEL(s(first(x0, x1)), cons(x2, cons(z0, z1))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), nil), MARK(nil)) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, 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A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), 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A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, 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c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), nil), MARK(nil)) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), 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A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), nil), MARK(nil)) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__first(mark(x0), mark(x1)), nil), MARK(nil)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), 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x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, 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c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), 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A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(A__SEL(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(A__SEL(first(mark(x0), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> 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c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) 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c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(s(z0)), cons(x1, x2)) -> c7(A__SEL(s(mark(z0)), mark(x2)), MARK(x2)) A__SEL(s(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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)), 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c7(MARK(sel(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (133) 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, from(z0))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(sel(x0, x1)), cons(x2, first(z0, z1))) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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, 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, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) 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, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(x3)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) 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mark(z1)), 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(0), cons(x1, cons(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) 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, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) 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, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (135) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c7(A__SEL(a__sel(mark(x0), mark(x1)), 0), MARK(0)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, 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x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) 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, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(x3)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), 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nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) 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, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(x3)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(0), cons(x1, x2)) -> c7(A__SEL(0, 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> 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c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (139) 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, from(z0))) -> c7(A__SEL(s(mark(x0)), a__from(mark(z0))), MARK(from(z0))) A__SEL(s(s(x0)), cons(x1, first(z0, z1))) -> c7(A__SEL(s(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), 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, nil)) -> c7(A__SEL(s(mark(x0)), nil), MARK(nil)) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), 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-> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), 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, nil)) -> c7(A__SEL(s(mark(x0)), nil), MARK(nil)) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) 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MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), 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, nil)) -> c7(A__SEL(s(mark(x0)), nil), MARK(nil)) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(s(x0)), cons(x1, 0)) -> c7(A__SEL(s(mark(x0)), 0), MARK(0)) A__SEL(s(s(x0)), cons(x1, nil)) -> c7(A__SEL(s(mark(x0)), nil), MARK(nil)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> 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x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), 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mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(x0)), cons(x1, s(z0))) -> c7(A__SEL(s(mark(x0)), s(mark(z0))), MARK(s(z0))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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(x0), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(cons(z0, z1)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) 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c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, 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A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_2, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2 ---------------------------------------- (145) 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, from(z0))) -> c7(A__SEL(0, a__from(mark(z0))), MARK(from(z0))) A__SEL(s(0), cons(x0, first(z0, z1))) -> c7(A__SEL(0, a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) A__SEL(s(0), cons(x0, nil)) -> c7(A__SEL(0, nil), MARK(nil)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), 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mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) A__SEL(s(0), cons(x0, nil)) -> c7(A__SEL(0, nil), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: A__SEL(s(0), cons(x0, 0)) -> c7(A__SEL(0, 0), MARK(0)) A__SEL(s(0), cons(x0, nil)) -> c7(A__SEL(0, nil), MARK(nil)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, 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x3)) -> c7(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), 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(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(A__SEL(0, s(mark(z0))), MARK(s(z0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), 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first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) 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__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), 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A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), 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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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, from(z0))) -> c10(A__FIRST(mark(x0), a__from(mark(z0))), MARK(x0)) by MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), from(x1))) -> c10(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(0, from(x1))) -> c10(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c10(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), 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c7(MARK(x3)) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), from(x1))) -> c10(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(0, from(x1))) -> c10(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c10(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), 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MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 0))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), 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mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, s(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 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MARK(sel(0, x3))) A__SEL(s(x0), cons(x1, sel(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), from(x1))) -> c10(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(0, from(x1))) -> c10(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c10(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, from(x1))) -> c10(A__FIRST(0, a__from(mark(x1))), MARK(0)) MARK(first(nil, from(x1))) -> c10(A__FIRST(nil, a__from(mark(x1))), MARK(nil)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> 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MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), 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c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 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A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, 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A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, 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from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), from(mark(x1))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), from(x1))) -> c10(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (155) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> 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cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, 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from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (157) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, first(z0, z1))) -> c10(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by MARK(first(x0, first(x1, x2))) -> c10(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, first(x1, x2))) -> c10(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c10(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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, 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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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), 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c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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), 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x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, x2))) -> c10(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), 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first(x1, x2))) -> c10(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, x2))) -> c10(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, first(x1, x2))) -> c10(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, first(x1, x2))) -> c10(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (159) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, first(x1, x2))) -> c10(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(nil)) MARK(first(0, first(x1, x2))) -> c10(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(0)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), 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mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, x2))) -> c10(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> 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z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, x2))) -> c10(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> 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MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), 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A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> 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MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> 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MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, 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a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, sel(z0, z1))) -> c10(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) by MARK(first(x0, sel(x1, x2))) -> c10(A__FIRST(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, sel(x1, x2))) -> c10(A__FIRST(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, sel(x1, x2))) -> c10(A__FIRST(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> 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cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), 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-> 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, x2))) -> c10(A__FIRST(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, sel(x1, x2))) -> c10(A__FIRST(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, sel(x1, x2))) -> c10(A__FIRST(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), 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c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, x2))) -> c10(A__FIRST(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(0, sel(x1, x2))) -> c10(A__FIRST(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, sel(x1, x2))) -> c10(A__FIRST(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(0, sel(x1, x2))) -> c10(A__FIRST(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(first(nil, sel(x1, x2))) -> c10(A__FIRST(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, 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c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, 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cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, 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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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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)) 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MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), 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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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, x2))) -> c10(A__FIRST(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) 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A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) 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A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> 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-> 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> 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a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, cons(z0, z1))) -> c10(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(0, cons(x1, x2))) -> c10(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c10(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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, 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c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, 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MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 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c10(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(0, cons(x1, x2))) -> c10(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c10(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), 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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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> 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cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), 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-> 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(0, cons(x1, x2))) -> c10(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) MARK(first(nil, cons(x1, x2))) -> c10(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(nil, cons(x1, x2))) -> c10(A__FIRST(nil, cons(mark(x1), x2)), MARK(nil)) MARK(first(0, cons(x1, x2))) -> c10(A__FIRST(0, cons(mark(x1), x2)), MARK(0)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) 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a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> 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cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, 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c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), 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c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(x0)) 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0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(from(z0), x1)) -> c10(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(from(z0))) by MARK(first(from(x0), from(z0))) -> c10(A__FIRST(a__from(mark(x0)), a__from(mark(z0))), MARK(from(x0))) MARK(first(from(x0), first(z0, z1))) -> c10(A__FIRST(a__from(mark(x0)), a__first(mark(z0), mark(z1))), MARK(from(x0))) MARK(first(from(x0), sel(z0, z1))) -> c10(A__FIRST(a__from(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(from(x0))) MARK(first(from(x0), cons(z0, z1))) -> c10(A__FIRST(a__from(mark(x0)), cons(mark(z0), z1)), MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(A__FIRST(a__from(mark(x0)), 0), MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(A__FIRST(a__from(mark(x0)), nil), MARK(from(x0))) MARK(first(from(x0), x1)) -> c10(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(from(x0))) MARK(first(from(x0), x1)) -> c10(A__FIRST(from(mark(x0)), mark(x1)), MARK(from(x0))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(0, x3))) -> 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a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(x0), s(z0))) -> c10(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(A__FIRST(a__from(mark(x0)), 0), MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(A__FIRST(a__from(mark(x0)), nil), MARK(from(x0))) MARK(first(from(x0), x1)) -> c10(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(from(x0))) MARK(first(from(x0), x1)) -> c10(A__FIRST(from(mark(x0)), mark(x1)), MARK(from(x0))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), 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MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) 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MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(first(z0, z1), x1)) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) by MARK(first(first(x0, x1), from(z0))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), a__from(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), first(z0, z1))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(x0, x1))) MARK(first(first(x0, x1), sel(z0, z1))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(first(x0, x1))) MARK(first(first(x0, x1), cons(z0, z1))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(first(x0, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, 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cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, 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mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> 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a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, 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c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, x1), s(z0))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), 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MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> 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-> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, x1), s(z0))) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(first(x0, x1))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), 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c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, 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c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), 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a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(sel(z0, z1), x1)) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) by MARK(first(sel(x0, x1), from(z0))) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), a__from(mark(z0))), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), first(z0, z1))) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), sel(z0, z1))) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), cons(z0, z1))) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), nil), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(A__FIRST(sel(mark(x0), mark(x1)), mark(x2)), MARK(sel(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), 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-> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), 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-> c7(A__SEL(mark(x0), cons(0, x3)), MARK(cons(0, x3))) A__SEL(s(x0), cons(x1, cons(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), 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MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), 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c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), 0), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(A__FIRST(a__sel(mark(x0), mark(x1)), nil), MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(A__FIRST(sel(mark(x0), mark(x1)), mark(x2)), MARK(sel(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 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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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_2, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(s(z0), x1)) -> c10(A__FIRST(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(first(s(x0), from(z0))) -> c10(A__FIRST(s(mark(x0)), a__from(mark(z0))), MARK(s(x0))) MARK(first(s(x0), first(z0, z1))) -> c10(A__FIRST(s(mark(x0)), a__first(mark(z0), mark(z1))), MARK(s(x0))) MARK(first(s(x0), sel(z0, z1))) -> c10(A__FIRST(s(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(s(x0))) MARK(first(s(x0), cons(z0, z1))) -> c10(A__FIRST(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(A__FIRST(s(mark(x0)), 0), MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(A__FIRST(s(mark(x0)), nil), MARK(s(x0))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), 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MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(x0), s(z0))) -> c10(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(A__FIRST(s(mark(x0)), 0), MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(A__FIRST(s(mark(x0)), nil), MARK(s(x0))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, 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MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) 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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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, from(z0))) -> c11(A__FIRST(mark(x0), a__from(mark(z0))), MARK(from(z0))) by MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(0, from(x1))) -> c11(A__FIRST(0, a__from(mark(x1))), MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(A__FIRST(nil, a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> 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c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(A__FIRST(cons(mark(z0), z1), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(0, from(x1))) -> c11(A__FIRST(0, a__from(mark(x1))), MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(A__FIRST(nil, a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, 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__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, 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MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, first(z0, z1))) -> c11(A__FIRST(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) by MARK(first(x0, first(x1, x2))) -> c11(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), 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cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, x2))) -> c11(A__FIRST(mark(x0), first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(A__FIRST(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(A__FIRST(0, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(A__FIRST(nil, a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> 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c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) 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MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, sel(z0, z1))) -> c11(A__FIRST(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) by MARK(first(x0, sel(x1, x2))) -> c11(A__FIRST(mark(x0), sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(A__FIRST(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(A__FIRST(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(A__FIRST(nil, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), 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c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, cons(x2, x3))) -> 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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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> 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c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(A__FIRST(mark(x0), sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(A__FIRST(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(A__FIRST(0, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(A__FIRST(nil, a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 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s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(x0, cons(z0, z1))) -> c11(A__FIRST(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(A__FIRST(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(A__FIRST(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> 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cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) 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A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, 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c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> 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cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(A__FIRST(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(A__FIRST(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(A__FIRST(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 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A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) 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c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), 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A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 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MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), 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a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), 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x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(x0), cons(x1, cons(x2, 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c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(from(z0), x1)) -> c11(A__FIRST(a__from(mark(z0)), mark(x1)), MARK(x1)) by MARK(first(from(x0), from(z0))) -> c11(A__FIRST(a__from(mark(x0)), a__from(mark(z0))), MARK(from(z0))) MARK(first(from(x0), first(z0, z1))) -> c11(A__FIRST(a__from(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(from(x0), sel(z0, z1))) -> c11(A__FIRST(a__from(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(from(x0), cons(z0, z1))) -> c11(A__FIRST(a__from(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(from(x0), s(z0))) -> c11(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), 0)) -> c11(A__FIRST(a__from(mark(x0)), 0), MARK(0)) MARK(first(from(x0), nil)) -> c11(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), x1)) -> c11(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c11(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> 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-> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), 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A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, sel(z0, z1)))) A__SEL(s(sel(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(sel(x0, cons(z0, z1)))) A__SEL(s(sel(x0, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, sel(z0, z1))), cons(x2, 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c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(x0), s(z0))) -> c11(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), 0)) -> c11(A__FIRST(a__from(mark(x0)), 0), MARK(0)) MARK(first(from(x0), nil)) -> c11(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), x1)) -> c11(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c11(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (209) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(from(x0), nil)) -> c11(A__FIRST(a__from(mark(x0)), nil), MARK(nil)) MARK(first(from(x0), 0)) -> c11(A__FIRST(a__from(mark(x0)), 0), MARK(0)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), 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mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(x0), s(z0))) -> c11(A__FIRST(a__from(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(A__FIRST(cons(mark(mark(x0)), from(s(mark(x0)))), mark(x1)), MARK(x1)) MARK(first(from(x0), x1)) -> c11(A__FIRST(from(mark(x0)), mark(x1)), MARK(x1)) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (211) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> 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cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, 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cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), 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MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, 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c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), 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cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (213) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(first(z0, z1), x1)) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(first(first(x0, x1), from(z0))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), a__from(mark(z0))), MARK(from(z0))) MARK(first(first(x0, x1), first(z0, z1))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(first(x0, x1), sel(z0, z1))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(first(x0, x1), cons(z0, z1))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(first(x0, x1), s(z0))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(first(x0, x1), 0)) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(first(x0, x1), nil)) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(first(x0, x1), x2)) -> c11(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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), 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x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, x1), s(z0))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(first(x0, x1), 0)) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(first(x0, x1), nil)) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(first(x0, x1), x2)) -> c11(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(first(x0, x1), 0)) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(first(x0, x1), nil)) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), nil), MARK(nil)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, 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mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), 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MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, x1), s(z0))) -> c11(A__FIRST(a__first(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(A__FIRST(first(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), 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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(x0), cons(x1, cons(0, x3))) -> c6(A__SEL(mark(x0), cons(0, x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), 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A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) 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c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), 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c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(sel(z0, z1), x1)) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) by MARK(first(sel(x0, x1), from(z0))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), a__from(mark(z0))), MARK(from(z0))) MARK(first(sel(x0, x1), first(z0, z1))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(sel(x0, x1), sel(z0, z1))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(sel(x0, x1), cons(z0, z1))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(sel(x0, x1), s(z0))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(sel(x0, x1), 0)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(sel(x0, x1), nil)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(sel(x0, x1), x2)) -> c11(A__FIRST(sel(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> 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c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(sel(x0, x1), 0)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(sel(x0, x1), nil)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(sel(x0, x1), x2)) -> c11(A__FIRST(sel(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> 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c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(sel(x0, x1), 0)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), 0), MARK(0)) MARK(first(sel(x0, x1), nil)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(sel(x0, x1), x2)) -> c11(A__FIRST(sel(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (221) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(sel(x0, x1), nil)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), nil), MARK(nil)) MARK(first(sel(x0, x1), 0)) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), 0), MARK(0)) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) 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c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), 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MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(A__FIRST(a__sel(mark(x0), mark(x1)), s(mark(z0))), MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(A__FIRST(sel(mark(x0), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (223) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> 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MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 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a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 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-> 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> 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from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, 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z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), 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MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_2, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2 ---------------------------------------- (225) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(first(s(z0), x1)) -> c11(A__FIRST(s(mark(z0)), mark(x1)), MARK(x1)) by MARK(first(s(x0), from(z0))) -> c11(A__FIRST(s(mark(x0)), a__from(mark(z0))), MARK(from(z0))) MARK(first(s(x0), first(z0, z1))) -> c11(A__FIRST(s(mark(x0)), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(first(s(x0), sel(z0, z1))) -> c11(A__FIRST(s(mark(x0)), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(first(s(x0), cons(z0, z1))) -> c11(A__FIRST(s(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(first(s(x0), s(z0))) -> c11(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(s(x0), 0)) -> c11(A__FIRST(s(mark(x0)), 0), MARK(0)) MARK(first(s(x0), nil)) -> c11(A__FIRST(s(mark(x0)), nil), MARK(nil)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> 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a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(first(x2, sel(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(first(x2, cons(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(first(s(z0), x3))) A__SEL(s(x0), cons(x1, first(0, x3))) -> c7(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(first(0, x3))) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c7(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(first(nil, x3))) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c7(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c7(A__SEL(0, a__first(mark(x2), mark(x3))), MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(nil), cons(x1, first(x2, x3))) -> c7(MARK(first(x2, x3))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(sel(x2, from(z0)))) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), MARK(sel(x2, first(z0, z1)))) 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, 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(x2, 0))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), 0)), MARK(sel(x2, 0))) A__SEL(s(x0), cons(x1, sel(x2, nil))) -> c7(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(sel(x2, nil))) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(sel(from(z0), x3))) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x3))), MARK(sel(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x3))), MARK(sel(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(sel(nil, x3))) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(sel(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(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(0), cons(x1, sel(x2, x3))) -> c7(A__SEL(0, 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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(x0), s(z0))) -> c11(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(s(x0), 0)) -> c11(A__FIRST(s(mark(x0)), 0), MARK(0)) MARK(first(s(x0), nil)) -> c11(A__FIRST(s(mark(x0)), nil), MARK(nil)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (227) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(first(s(x0), nil)) -> c11(A__FIRST(s(mark(x0)), nil), MARK(nil)) MARK(first(s(x0), 0)) -> c11(A__FIRST(s(mark(x0)), 0), MARK(0)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> 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mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, 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first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(x0), s(z0))) -> c11(A__FIRST(s(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) 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MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), 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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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, from(z0))) -> c12(A__SEL(mark(x0), a__from(mark(z0))), MARK(x0)) by MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), from(mark(x1))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), from(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1))), MARK(0)) MARK(sel(nil, from(x1))) -> c12(A__SEL(nil, a__from(mark(x1))), MARK(nil)) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), 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0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), from(mark(x1))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), 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c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), 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c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), from(mark(x1))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), from(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1))), MARK(0)) MARK(sel(nil, from(x1))) -> c12(A__SEL(nil, a__from(mark(x1))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (233) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(sel(nil, from(x1))) -> c12(A__SEL(nil, a__from(mark(x1))), MARK(nil)) ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) 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MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), 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0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) 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z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) 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c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), from(mark(x1))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), from(x1))) -> c12(A__SEL(cons(mark(z0), z1), a__from(mark(x1))), MARK(cons(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1))), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (235) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), 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MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 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A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) 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c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), 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A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c7(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(0), cons(x1, from(x2))) -> c7(A__SEL(0, a__from(mark(x2))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(nil), cons(x1, from(x2))) -> c7(MARK(from(x2))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(first(x2, from(z0)))) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(first(x2, first(z0, z1)))) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 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x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (237) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(sel(x0, first(z0, z1))) -> c12(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(x0)) by MARK(sel(x0, first(x1, x2))) -> c12(A__SEL(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, first(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, first(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, 0))) -> c12(A__SEL(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(sel(x0, first(x1, nil))) -> c12(A__SEL(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(sel(x0, first(from(z0), x2))) -> c12(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, first(s(z0), x2))) -> c12(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(0, x2))) -> c12(A__SEL(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(sel(nil, first(x1, x2))) -> c12(A__SEL(nil, a__first(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, 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c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, 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c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) 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first(s(z0), x2))) -> c12(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(0, x2))) -> c12(A__SEL(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(sel(nil, first(x1, x2))) -> c12(A__SEL(nil, a__first(mark(x1), mark(x2))), MARK(nil)) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, 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A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), 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A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), s(mark(z0))), 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, nil)), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(s(mark(z0)), 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(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__sel(nil, 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(s(from(z0))), cons(x1, x2)) -> c7(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(s(a__first(mark(z0), mark(z1))), 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(s(z0))), cons(x1, x2)) -> c7(A__SEL(s(s(mark(z0))), 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(nil)), cons(x1, x2)) -> c7(A__SEL(s(nil), mark(x2)), MARK(x2)) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(0), cons(x0, s(z0))) -> c7(MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(first(x0, from(from(z0)))) -> c10(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(first(x0, from(first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, from(cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, from(s(z0)))) -> c10(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(first(x0, from(0))) -> c10(A__FIRST(mark(x0), a__from(0)), MARK(x0)) MARK(first(x0, from(nil))) -> c10(A__FIRST(mark(x0), a__from(nil)), MARK(x0)) MARK(first(from(z0), from(x1))) -> c10(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(first(first(z0, z1), from(x1))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), from(x1))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(first(s(z0), from(x1))) -> c10(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(first(x0, from(x1))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), from(x1))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, first(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, first(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, first(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, first(x1, 0))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(first(x0, first(x1, nil))) -> c10(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(first(x0, first(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, first(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, first(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, first(0, x2))) -> c10(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(first(x0, first(nil, x2))) -> c10(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), first(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), first(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), first(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) MARK(sel(x0, first(x1, x2))) -> c12(A__SEL(mark(x0), first(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, first(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, first(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, 0))) -> c12(A__SEL(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(sel(x0, first(x1, nil))) -> c12(A__SEL(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(sel(x0, first(from(z0), x2))) -> c12(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, first(s(z0), x2))) -> c12(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(0, x2))) -> c12(A__SEL(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2))), MARK(0)) MARK(sel(nil, first(x1, x2))) -> c12(A__SEL(nil, a__first(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (239) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(sel(nil, first(x1, x2))) -> c12(A__SEL(nil, a__first(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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(s(z0))), cons(x1, x2)) -> c6(A__SEL(s(s(mark(z0))), mark(x2)), MARK(s(s(z0)))) A__SEL(s(s(0)), cons(x1, x2)) -> c6(A__SEL(s(0), mark(x2)), MARK(s(0))) A__SEL(s(s(nil)), cons(x1, x2)) -> c6(A__SEL(s(nil), mark(x2)), MARK(s(nil))) A__SEL(s(s(x0)), cons(x1, x2)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, s(z0))) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, 0)) -> c6(MARK(s(x0))) A__SEL(s(s(x0)), cons(x1, nil)) -> c6(MARK(s(x0))) A__SEL(s(x0), cons(x1, from(x2))) -> c7(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(from(x2))) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c7(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c7(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c7(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) A__SEL(s(x0), cons(x1, from(0))) -> c7(A__SEL(mark(x0), a__from(0)), MARK(from(0))) A__SEL(s(x0), cons(x1, from(nil))) -> c7(A__SEL(mark(x0), a__from(nil)), MARK(from(nil))) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c7(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(from(x2))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c7(A__SEL(a__sel(mark(z0), mark(z1)), 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cons(x1, first(x2, s(z0)))) -> c7(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(first(x2, s(z0)))) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c7(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(first(x2, 0))) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c7(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(first(x2, nil))) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c7(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(first(from(z0), x3))) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(first(first(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(first(sel(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c7(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(first(cons(z0, z1), x3))) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c7(A__SEL(mark(x0), a__first(s(mark(z0)), 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mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), 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a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__first(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (241) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> 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c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), 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MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) MARK(sel(x0, first(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, 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-> c12(A__SEL(0, a__first(mark(x1), mark(x2)))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, sel(z0, z1))) -> c12(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(x0)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), 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mark(x2))), MARK(s(z0))) MARK(first(x0, first(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), first(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, sel(x1, from(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, first(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(first(x0, sel(x1, s(z0)))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(first(x0, sel(x1, 0))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(first(x0, sel(x1, nil))) -> c10(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(first(x0, sel(from(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(first(x0, sel(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(first(x0, sel(s(z0), x2))) -> c10(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(first(x0, sel(0, x2))) -> c10(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(first(x0, sel(nil, x2))) -> c10(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(first(from(z0), sel(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(first(first(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(first(s(z0), sel(x1, x2))) -> c10(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(first(x0, sel(x1, x2))) -> c10(MARK(x0)) MARK(first(cons(z0, z1), sel(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(x0, cons(from(z0), x2))) -> c10(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(first(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(sel(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(first(x0, cons(cons(z0, z1), x2))) -> c10(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(first(x0, cons(s(z0), x2))) -> c10(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(first(x0, cons(0, x2))) -> c10(A__FIRST(mark(x0), cons(0, x2)), MARK(x0)) MARK(first(x0, cons(nil, x2))) -> c10(A__FIRST(mark(x0), cons(nil, x2)), MARK(x0)) MARK(first(from(z0), cons(x1, x2))) -> c10(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, from(first(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, from(cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, from(s(z0)))) -> c12(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) MARK(sel(x0, from(0))) -> c12(A__SEL(mark(x0), a__from(0)), MARK(x0)) MARK(sel(x0, from(nil))) -> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) MARK(sel(x0, first(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, first(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, 0))) -> c12(A__SEL(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(sel(x0, first(x1, nil))) -> c12(A__SEL(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(sel(x0, first(from(z0), x2))) -> c12(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, first(s(z0), x2))) -> c12(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(0, x2))) -> c12(A__SEL(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, first(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (243) 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(x0)) by MARK(sel(x0, sel(x1, x2))) -> c12(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, nil))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(sel(x0, sel(from(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(nil, x2))) -> c12(A__SEL(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), sel(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) 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(z0, z1))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(sel(nil, sel(x1, x2))) -> c12(A__SEL(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> 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-> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), 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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(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(nil), cons(x1, sel(x2, x3))) -> c7(MARK(sel(x2, x3))) A__SEL(s(x0), cons(x1, cons(from(z0), x3))) -> c7(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(cons(from(z0), x3))) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c7(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), x3)), MARK(cons(first(z0, z1), 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(s(z0), x3))) -> c7(A__SEL(mark(x0), cons(s(mark(z0)), x3)), MARK(cons(s(z0), 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(nil, x3))) -> c7(A__SEL(mark(x0), cons(nil, x3)), MARK(cons(nil, x3))) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(cons(x2, x3))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c7(A__SEL(a__first(mark(z0), mark(z1)), 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(s(z0)), cons(x1, cons(x2, x3))) -> c7(A__SEL(s(mark(z0)), 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(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(nil), cons(x1, cons(x2, x3))) -> c7(MARK(cons(x2, x3))) A__SEL(s(from(from(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c7(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(x2)) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c7(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(x2)) A__SEL(s(from(0)), cons(x1, x2)) -> c7(A__SEL(a__from(0), mark(x2)), MARK(x2)) A__SEL(s(from(nil)), cons(x1, x2)) -> c7(A__SEL(a__from(nil), mark(x2)), MARK(x2)) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(from(x0)), cons(x1, x2)) -> c7(MARK(x2)) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(x3)) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c7(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(x3)) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c7(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c7(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(x3)) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c7(MARK(s(z0))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c7(MARK(x3)) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(x3)) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c7(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), 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, 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-> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, first(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2)))) MARK(sel(x0, sel(x1, x2))) -> c12(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, nil))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(sel(x0, sel(from(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(nil, x2))) -> c12(A__SEL(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), sel(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) 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(z0, z1))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(0)) MARK(sel(nil, sel(x1, x2))) -> c12(A__SEL(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (245) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(sel(nil, sel(x1, x2))) -> c12(A__SEL(nil, a__sel(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), 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A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), cons(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), cons(nil, x3)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), cons(mark(x2), x3)), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, cons(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), cons(mark(x2), x3)), MARK(first(z0, z1))) 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(from(from(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(a__from(mark(z0))), mark(x2)), MARK(from(from(z0)))) A__SEL(s(from(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__first(mark(z0), mark(z1))), mark(x2)), MARK(from(first(z0, z1)))) A__SEL(s(from(sel(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(a__sel(mark(z0), mark(z1))), mark(x2)), MARK(from(sel(z0, z1)))) A__SEL(s(from(cons(z0, z1))), cons(x1, x2)) -> c6(A__SEL(a__from(cons(mark(z0), z1)), mark(x2)), MARK(from(cons(z0, z1)))) A__SEL(s(from(s(z0))), cons(x1, x2)) -> c6(A__SEL(a__from(s(mark(z0))), mark(x2)), MARK(from(s(z0)))) A__SEL(s(from(0)), cons(x1, x2)) -> c6(A__SEL(a__from(0), mark(x2)), MARK(from(0))) A__SEL(s(from(nil)), cons(x1, x2)) -> c6(A__SEL(a__from(nil), mark(x2)), MARK(from(nil))) A__SEL(s(from(x0)), cons(x1, x2)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, s(z0))) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, 0)) -> c6(MARK(from(x0))) A__SEL(s(from(x0)), cons(x1, nil)) -> c6(MARK(from(x0))) A__SEL(s(first(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__from(mark(z0))), mark(x3)), MARK(first(x0, from(z0)))) A__SEL(s(first(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, first(z0, z1)))) A__SEL(s(first(x0, sel(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x3)), MARK(first(x0, sel(z0, z1)))) A__SEL(s(first(x0, cons(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), cons(mark(z0), z1)), mark(x3)), MARK(first(x0, cons(z0, z1)))) A__SEL(s(first(x0, s(z0))), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), s(mark(z0))), mark(x3)), MARK(first(x0, s(z0)))) A__SEL(s(first(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), 0), mark(x3)), MARK(first(x0, 0))) A__SEL(s(first(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__first(mark(x0), nil), mark(x3)), MARK(first(x0, nil))) A__SEL(s(first(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(first(from(z0), x1))) A__SEL(s(first(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(first(z0, z1), x1))) A__SEL(s(first(sel(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(first(sel(z0, z1), x1))) A__SEL(s(first(cons(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(cons(mark(z0), z1), mark(x1)), mark(x3)), MARK(first(cons(z0, z1), x1))) A__SEL(s(first(s(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__first(s(mark(z0)), mark(x1)), mark(x3)), MARK(first(s(z0), x1))) A__SEL(s(first(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(0, mark(x1)), mark(x3)), MARK(first(0, x1))) A__SEL(s(first(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__first(nil, mark(x1)), mark(x3)), MARK(first(nil, x1))) A__SEL(s(first(x0, x1)), cons(x2, s(z0))) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, 0)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, nil)) -> c6(MARK(first(x0, x1))) A__SEL(s(first(x0, x1)), cons(x2, x3)) -> c6(MARK(first(x0, x1))) A__SEL(s(sel(x0, from(z0))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__from(mark(z0))), mark(x3)), MARK(sel(x0, from(z0)))) A__SEL(s(sel(x0, first(z0, z1))), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x3)), MARK(sel(x0, first(z0, z1)))) 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, 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(x0, 0)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), 0), mark(x3)), MARK(sel(x0, 0))) A__SEL(s(sel(x0, nil)), cons(x2, x3)) -> c6(A__SEL(a__sel(mark(x0), nil), mark(x3)), MARK(sel(x0, nil))) A__SEL(s(sel(from(z0), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__from(mark(z0)), mark(x1)), mark(x3)), MARK(sel(from(z0), x1))) A__SEL(s(sel(first(z0, z1), x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x3)), MARK(sel(first(z0, z1), 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(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(0, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(0, mark(x1)), mark(x3)), MARK(sel(0, x1))) A__SEL(s(sel(nil, x1)), cons(x2, x3)) -> c6(A__SEL(a__sel(nil, mark(x1)), mark(x3)), MARK(sel(nil, x1))) A__SEL(s(sel(x0, x1)), cons(x2, s(z0))) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, 0)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, nil)) -> c6(MARK(sel(x0, x1))) A__SEL(s(sel(x0, x1)), cons(x2, x3)) -> c6(MARK(sel(x0, x1))) A__SEL(s(s(from(z0))), cons(x1, x2)) -> c6(A__SEL(s(a__from(mark(z0))), mark(x2)), MARK(s(from(z0)))) A__SEL(s(s(first(z0, z1))), cons(x1, x2)) -> c6(A__SEL(s(a__first(mark(z0), mark(z1))), mark(x2)), MARK(s(first(z0, z1)))) 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)))) 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MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), 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a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, first(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2)))) MARK(sel(x0, sel(x1, x2))) -> c12(A__SEL(mark(x0), sel(mark(x1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, nil))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(sel(x0, sel(from(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(nil, x2))) -> c12(A__SEL(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), sel(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) 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(z0, z1))) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(A__SEL(cons(mark(z0), z1), a__sel(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2))), MARK(0)) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2 ---------------------------------------- (247) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: a__from(z0) -> cons(mark(z0), from(s(z0))) a__from(z0) -> from(z0) a__first(0, z0) -> nil a__first(s(z0), cons(z1, z2)) -> cons(mark(z1), first(z0, z2)) a__first(z0, z1) -> first(z0, z1) 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(from(z0)) -> a__from(mark(z0)) mark(first(z0, z1)) -> a__first(mark(z0), mark(z1)) mark(sel(z0, z1)) -> a__sel(mark(z0), mark(z1)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 mark(nil) -> nil Tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) MARK(sel(x0, from(z0))) -> c13(A__SEL(mark(x0), a__from(mark(z0))), MARK(from(z0))) MARK(sel(x0, first(z0, z1))) -> c13(A__SEL(mark(x0), a__first(mark(z0), mark(z1))), MARK(first(z0, z1))) MARK(sel(x0, sel(z0, z1))) -> c13(A__SEL(mark(x0), a__sel(mark(z0), mark(z1))), MARK(sel(z0, z1))) MARK(sel(x0, cons(z0, z1))) -> c13(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(sel(from(z0), x1)) -> c13(A__SEL(a__from(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(first(z0, z1), x1)) -> c13(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(sel(z0, z1), x1)) -> c13(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(sel(s(z0), x1)) -> c13(A__SEL(s(mark(z0)), mark(x1)), MARK(x1)) MARK(sel(0, x1)) -> c13(A__SEL(0, mark(x1)), MARK(x1)) MARK(sel(x0, s(z0))) -> c13(MARK(s(z0))) MARK(sel(cons(z0, z1), x1)) -> c13(MARK(x1)) MARK(sel(nil, x1)) -> c13(MARK(x1)) A__SEL(s(x0), cons(x1, from(x2))) -> c6(A__SEL(mark(x0), cons(mark(mark(x2)), from(s(mark(x2))))), MARK(x0)) A__SEL(s(x0), cons(x1, from(from(z0)))) -> c6(A__SEL(mark(x0), a__from(a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(first(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__from(cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, from(s(z0)))) -> c6(A__SEL(mark(x0), a__from(s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, from(0))) -> c6(A__SEL(mark(x0), a__from(0)), MARK(x0)) A__SEL(s(x0), cons(x1, from(nil))) -> c6(A__SEL(mark(x0), a__from(nil)), MARK(x0)) A__SEL(s(from(z0)), cons(x1, from(x2))) -> c6(A__SEL(a__from(mark(z0)), a__from(mark(x2))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x2))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, from(x2))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x2))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, from(x2))) -> c6(A__SEL(s(mark(z0)), a__from(mark(x2))), MARK(s(z0))) A__SEL(s(x0), cons(x1, from(x2))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, from(x2))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, from(x2))) -> c6(A__SEL(0, a__from(mark(x2)))) A__SEL(s(x0), cons(x1, first(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__first(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, sel(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), a__sel(mark(z0), mark(z1)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, cons(z0, z1)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), cons(mark(z0), z1))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, s(z0)))) -> c6(A__SEL(mark(x0), a__first(mark(x2), s(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, 0))) -> c6(A__SEL(mark(x0), a__first(mark(x2), 0)), MARK(x0)) A__SEL(s(x0), cons(x1, first(x2, nil))) -> c6(A__SEL(mark(x0), a__first(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, first(from(z0), x3))) -> c6(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(sel(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(cons(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(s(z0), x3))) -> c6(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(0, x3))) -> c6(A__SEL(mark(x0), a__first(0, mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, first(nil, x3))) -> c6(A__SEL(mark(x0), a__first(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__first(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(first(z0, z1))) A__SEL(s(sel(z0, z1)), cons(x1, first(x2, x3))) -> c6(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x2), mark(x3))), MARK(sel(z0, z1))) A__SEL(s(s(z0)), cons(x1, first(x2, x3))) -> c6(A__SEL(s(mark(z0)), a__first(mark(x2), mark(x3))), MARK(s(z0))) A__SEL(s(x0), cons(x1, first(x2, x3))) -> c6(MARK(x0)) A__SEL(s(cons(z0, z1)), cons(x1, first(x2, x3))) -> c6(MARK(cons(z0, z1))) A__SEL(s(0), cons(x1, first(x2, x3))) -> c6(A__SEL(0, a__first(mark(x2), mark(x3)))) A__SEL(s(x0), cons(x1, sel(x2, from(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__from(mark(z0)))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(x2, first(z0, z1)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), a__first(mark(z0), mark(z1)))), 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, s(z0)))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), s(mark(z0)))), 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, nil))) -> c6(A__SEL(mark(x0), a__sel(mark(x2), nil)), MARK(x0)) A__SEL(s(x0), cons(x1, sel(from(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x3))), MARK(x0)) A__SEL(s(x0), cons(x1, sel(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), 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(s(z0), x3))) -> c6(A__SEL(mark(x0), a__sel(s(mark(z0)), 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(nil, x3))) -> c6(A__SEL(mark(x0), a__sel(nil, mark(x3))), MARK(x0)) A__SEL(s(from(z0)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__from(mark(z0)), a__sel(mark(x2), mark(x3))), MARK(from(z0))) A__SEL(s(first(z0, z1)), cons(x1, sel(x2, x3))) -> c6(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x2), mark(x3))), MARK(first(z0, z1))) 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(from(z0), x3))) -> c6(A__SEL(mark(x0), cons(a__from(mark(z0)), x3)), MARK(x0)) A__SEL(s(x0), cons(x1, cons(first(z0, z1), x3))) -> c6(A__SEL(mark(x0), cons(a__first(mark(z0), mark(z1)), 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)), 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cons(mark(x1), x2)), MARK(from(z0))) MARK(first(first(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(first(z0, z1))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c10(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(sel(z0, z1))) MARK(first(s(z0), cons(x1, x2))) -> c10(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c10(MARK(cons(z0, z1))) MARK(first(from(from(z0)), x1)) -> c10(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(from(from(z0)))) MARK(first(from(first(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(from(first(z0, z1)))) MARK(first(from(sel(z0, z1)), x1)) -> c10(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(from(sel(z0, z1)))) MARK(first(from(cons(z0, z1)), x1)) -> c10(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(from(cons(z0, z1)))) MARK(first(from(s(z0)), x1)) -> c10(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(from(s(z0)))) MARK(first(from(0), x1)) -> c10(A__FIRST(a__from(0), mark(x1)), MARK(from(0))) MARK(first(from(nil), x1)) -> c10(A__FIRST(a__from(nil), mark(x1)), MARK(from(nil))) MARK(first(from(x0), x1)) -> c10(MARK(from(x0))) MARK(first(from(x0), s(z0))) -> c10(MARK(from(x0))) MARK(first(from(x0), 0)) -> c10(MARK(from(x0))) MARK(first(from(x0), nil)) -> c10(MARK(from(x0))) MARK(first(first(x0, from(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(first(x0, from(z0)))) MARK(first(first(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, first(z0, z1)))) MARK(first(first(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(first(x0, sel(z0, z1)))) MARK(first(first(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(first(x0, cons(z0, z1)))) MARK(first(first(x0, s(z0)), x2)) -> c10(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(first(x0, s(z0)))) MARK(first(first(x0, 0), x2)) -> c10(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(first(x0, 0))) MARK(first(first(x0, nil), x2)) -> c10(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(first(x0, nil))) MARK(first(first(from(z0), x1), x2)) -> c10(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(first(from(z0), x1))) MARK(first(first(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(first(z0, z1), x1))) MARK(first(first(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(first(sel(z0, z1), x1))) MARK(first(first(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(first(cons(z0, z1), x1))) MARK(first(first(s(z0), x1), x2)) -> c10(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(first(s(z0), x1))) MARK(first(first(0, x1), x2)) -> c10(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(first(0, x1))) MARK(first(first(nil, x1), x2)) -> c10(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(first(nil, x1))) MARK(first(first(x0, x1), s(z0))) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), 0)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), nil)) -> c10(MARK(first(x0, x1))) MARK(first(first(x0, x1), x2)) -> c10(MARK(first(x0, x1))) MARK(first(sel(x0, from(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(sel(x0, from(z0)))) MARK(first(sel(x0, first(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, first(z0, z1)))) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(sel(x0, sel(z0, z1)))) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c10(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(sel(x0, cons(z0, z1)))) MARK(first(sel(x0, s(z0)), x2)) -> c10(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(sel(x0, s(z0)))) MARK(first(sel(x0, 0), x2)) -> c10(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(sel(x0, 0))) MARK(first(sel(x0, nil), x2)) -> c10(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(sel(x0, nil))) MARK(first(sel(from(z0), x1), x2)) -> c10(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(sel(from(z0), x1))) MARK(first(sel(first(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(first(z0, z1), x1))) MARK(first(sel(sel(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(sel(sel(z0, z1), x1))) MARK(first(sel(cons(z0, z1), x1), x2)) -> c10(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(sel(cons(z0, z1), x1))) MARK(first(sel(s(z0), x1), x2)) -> c10(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(sel(s(z0), x1))) MARK(first(sel(0, x1), x2)) -> c10(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(sel(0, x1))) MARK(first(sel(nil, x1), x2)) -> c10(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(sel(nil, x1))) MARK(first(sel(x0, x1), s(z0))) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), 0)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), nil)) -> c10(MARK(sel(x0, x1))) MARK(first(sel(x0, x1), x2)) -> c10(MARK(sel(x0, x1))) MARK(first(s(from(z0)), x1)) -> c10(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(s(from(z0)))) MARK(first(s(first(z0, z1)), x1)) -> c10(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(s(first(z0, z1)))) MARK(first(s(sel(z0, z1)), x1)) -> c10(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(s(sel(z0, z1)))) MARK(first(s(cons(z0, z1)), x1)) -> c10(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(first(s(s(z0)), x1)) -> c10(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(first(s(0), x1)) -> c10(A__FIRST(s(0), mark(x1)), MARK(s(0))) MARK(first(s(nil), x1)) -> c10(A__FIRST(s(nil), mark(x1)), MARK(s(nil))) MARK(first(s(x0), x1)) -> c10(MARK(s(x0))) MARK(first(s(x0), s(z0))) -> c10(MARK(s(x0))) MARK(first(s(x0), 0)) -> c10(MARK(s(x0))) MARK(first(s(x0), nil)) -> c10(MARK(s(x0))) MARK(first(x0, from(x1))) -> c11(A__FIRST(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(from(x1))) MARK(first(x0, from(from(z0)))) -> c11(A__FIRST(mark(x0), a__from(a__from(mark(z0)))), MARK(from(from(z0)))) MARK(first(x0, from(first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__first(mark(z0), mark(z1)))), MARK(from(first(z0, z1)))) MARK(first(x0, from(sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(a__sel(mark(z0), mark(z1)))), MARK(from(sel(z0, z1)))) MARK(first(x0, from(cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__from(cons(mark(z0), z1))), MARK(from(cons(z0, z1)))) MARK(first(x0, from(s(z0)))) -> c11(A__FIRST(mark(x0), a__from(s(mark(z0)))), MARK(from(s(z0)))) MARK(first(x0, from(0))) -> c11(A__FIRST(mark(x0), a__from(0)), MARK(from(0))) MARK(first(x0, from(nil))) -> c11(A__FIRST(mark(x0), a__from(nil)), MARK(from(nil))) MARK(first(from(z0), from(x1))) -> c11(A__FIRST(a__from(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(first(z0, z1), from(x1))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(sel(z0, z1), from(x1))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(from(x1))) MARK(first(s(z0), from(x1))) -> c11(A__FIRST(s(mark(z0)), a__from(mark(x1))), MARK(from(x1))) MARK(first(x0, from(x1))) -> c11(MARK(from(x1))) MARK(first(cons(z0, z1), from(x1))) -> c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, nil))) MARK(first(x0, first(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(first(from(z0), x2))) MARK(first(x0, first(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(first(first(z0, z1), x2))) MARK(first(x0, first(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(first(sel(z0, z1), x2))) MARK(first(x0, first(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(first(cons(z0, z1), x2))) MARK(first(x0, first(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(first(s(z0), x2))) MARK(first(x0, first(0, x2))) -> c11(A__FIRST(mark(x0), a__first(0, mark(x2))), MARK(first(0, x2))) MARK(first(x0, first(nil, x2))) -> c11(A__FIRST(mark(x0), a__first(nil, mark(x2))), MARK(first(nil, x2))) MARK(first(from(z0), first(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(first(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(sel(z0, z1), first(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(s(z0), first(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(first(x1, x2))) MARK(first(x0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(cons(z0, z1), first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(0, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(nil, first(x1, x2))) -> c11(MARK(first(x1, x2))) MARK(first(x0, sel(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(sel(x1, from(z0)))) MARK(first(x0, sel(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(sel(x1, first(z0, z1)))) MARK(first(x0, sel(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(sel(x1, sel(z0, z1)))) MARK(first(x0, sel(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(sel(x1, cons(z0, z1)))) MARK(first(x0, sel(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(sel(x1, s(z0)))) MARK(first(x0, sel(x1, 0))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), 0)), MARK(sel(x1, 0))) MARK(first(x0, sel(x1, nil))) -> c11(A__FIRST(mark(x0), a__sel(mark(x1), nil)), MARK(sel(x1, nil))) MARK(first(x0, sel(from(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(sel(from(z0), x2))) MARK(first(x0, sel(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(sel(first(z0, z1), x2))) MARK(first(x0, sel(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(sel(sel(z0, z1), x2))) MARK(first(x0, sel(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(sel(cons(z0, z1), x2))) MARK(first(x0, sel(s(z0), x2))) -> c11(A__FIRST(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(sel(s(z0), x2))) MARK(first(x0, sel(0, x2))) -> c11(A__FIRST(mark(x0), a__sel(0, mark(x2))), MARK(sel(0, x2))) MARK(first(x0, sel(nil, x2))) -> c11(A__FIRST(mark(x0), a__sel(nil, mark(x2))), MARK(sel(nil, x2))) MARK(first(from(z0), sel(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(first(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(sel(z0, z1), sel(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(s(z0), sel(x1, x2))) -> c11(A__FIRST(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(sel(x1, x2))) MARK(first(x0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(cons(z0, z1), sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(0, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(nil, sel(x1, x2))) -> c11(MARK(sel(x1, x2))) MARK(first(x0, cons(from(z0), x2))) -> c11(A__FIRST(mark(x0), cons(a__from(mark(z0)), x2)), MARK(cons(from(z0), x2))) MARK(first(x0, cons(first(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__first(mark(z0), mark(z1)), x2)), MARK(cons(first(z0, z1), x2))) MARK(first(x0, cons(sel(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(a__sel(mark(z0), mark(z1)), x2)), MARK(cons(sel(z0, z1), x2))) MARK(first(x0, cons(cons(z0, z1), x2))) -> c11(A__FIRST(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(first(x0, cons(s(z0), x2))) -> c11(A__FIRST(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(first(x0, cons(0, x2))) -> c11(A__FIRST(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(first(x0, cons(nil, x2))) -> c11(A__FIRST(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(first(from(z0), cons(x1, x2))) -> c11(A__FIRST(a__from(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(first(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__first(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(sel(z0, z1), cons(x1, x2))) -> c11(A__FIRST(a__sel(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(s(z0), cons(x1, x2))) -> c11(A__FIRST(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(first(x0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(cons(z0, z1), cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(0, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(nil, cons(x1, x2))) -> c11(MARK(cons(x1, x2))) MARK(first(from(from(z0)), x1)) -> c11(A__FIRST(a__from(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(first(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(sel(z0, z1)), x1)) -> c11(A__FIRST(a__from(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(from(cons(z0, z1)), x1)) -> c11(A__FIRST(a__from(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(from(s(z0)), x1)) -> c11(A__FIRST(a__from(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(from(0), x1)) -> c11(A__FIRST(a__from(0), mark(x1)), MARK(x1)) MARK(first(from(nil), x1)) -> c11(A__FIRST(a__from(nil), mark(x1)), MARK(x1)) MARK(first(from(x0), s(z0))) -> c11(MARK(s(z0))) MARK(first(from(x0), x1)) -> c11(MARK(x1)) MARK(first(first(x0, from(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(first(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__first(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(first(x0, s(z0)), x2)) -> c11(A__FIRST(a__first(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(first(x0, 0), x2)) -> c11(A__FIRST(a__first(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(first(x0, nil), x2)) -> c11(A__FIRST(a__first(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(first(from(z0), x1), x2)) -> c11(A__FIRST(a__first(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__first(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(s(z0), x1), x2)) -> c11(A__FIRST(a__first(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(0, x1), x2)) -> c11(A__FIRST(a__first(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(nil, x1), x2)) -> c11(A__FIRST(a__first(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(first(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(first(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(sel(x0, from(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__from(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, first(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__first(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, sel(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), a__sel(mark(z0), mark(z1))), mark(x2)), MARK(x2)) MARK(first(sel(x0, cons(z0, z1)), x2)) -> c11(A__FIRST(a__sel(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, s(z0)), x2)) -> c11(A__FIRST(a__sel(mark(x0), s(mark(z0))), mark(x2)), MARK(x2)) MARK(first(sel(x0, 0), x2)) -> c11(A__FIRST(a__sel(mark(x0), 0), mark(x2)), MARK(x2)) MARK(first(sel(x0, nil), x2)) -> c11(A__FIRST(a__sel(mark(x0), nil), mark(x2)), MARK(x2)) MARK(first(sel(from(z0), x1), x2)) -> c11(A__FIRST(a__sel(a__from(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(first(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__first(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(sel(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(a__sel(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(cons(z0, z1), x1), x2)) -> c11(A__FIRST(a__sel(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(s(z0), x1), x2)) -> c11(A__FIRST(a__sel(s(mark(z0)), mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(0, x1), x2)) -> c11(A__FIRST(a__sel(0, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(nil, x1), x2)) -> c11(A__FIRST(a__sel(nil, mark(x1)), mark(x2)), MARK(x2)) MARK(first(sel(x0, x1), s(z0))) -> c11(MARK(s(z0))) MARK(first(sel(x0, x1), x2)) -> c11(MARK(x2)) MARK(first(s(from(z0)), x1)) -> c11(A__FIRST(s(a__from(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(first(z0, z1)), x1)) -> c11(A__FIRST(s(a__first(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(sel(z0, z1)), x1)) -> c11(A__FIRST(s(a__sel(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(first(s(cons(z0, z1)), x1)) -> c11(A__FIRST(s(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(first(s(s(z0)), x1)) -> c11(A__FIRST(s(s(mark(z0))), mark(x1)), MARK(x1)) MARK(first(s(0), x1)) -> c11(A__FIRST(s(0), mark(x1)), MARK(x1)) MARK(first(s(nil), x1)) -> c11(A__FIRST(s(nil), mark(x1)), MARK(x1)) MARK(first(s(x0), s(z0))) -> c11(MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(A__SEL(mark(x0), cons(mark(mark(x1)), from(s(mark(x1))))), MARK(x0)) MARK(sel(x0, from(from(z0)))) -> c12(A__SEL(mark(x0), 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MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) MARK(sel(x0, first(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, first(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, 0))) -> c12(A__SEL(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(sel(x0, first(x1, nil))) -> c12(A__SEL(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(sel(x0, first(from(z0), x2))) -> c12(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, first(s(z0), x2))) -> c12(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(0, x2))) -> c12(A__SEL(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, first(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2)))) MARK(sel(x0, sel(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, nil))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(sel(x0, sel(from(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(nil, x2))) -> c12(A__SEL(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), sel(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) 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(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2)))) S tuples: A__FROM(z0) -> c(MARK(z0)) A__FIRST(s(z0), cons(z1, z2)) -> c3(MARK(z1)) A__SEL(0, cons(z0, z1)) -> c5(MARK(z0)) MARK(from(z0)) -> c9(A__FROM(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c14(MARK(z0)) MARK(s(z0)) -> c15(MARK(z0)) A__SEL(s(x0), cons(x1, s(z0))) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, 0)) -> c6(MARK(x0)) A__SEL(s(x0), cons(x1, nil)) -> 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)) A__SEL(s(nil), cons(x1, x2)) -> c7(MARK(x2)) MARK(first(x0, s(z0))) -> c10(MARK(x0)) MARK(first(x0, 0)) -> c10(MARK(x0)) MARK(first(x0, nil)) -> c10(MARK(x0)) MARK(first(cons(z0, z1), x1)) -> c10(MARK(cons(z0, z1))) MARK(first(x0, s(z0))) -> c11(MARK(s(z0))) MARK(first(cons(z0, z1), x1)) -> c11(MARK(x1)) MARK(first(0, x1)) -> c11(MARK(x1)) MARK(first(nil, x1)) -> c11(MARK(x1)) MARK(sel(x0, cons(z0, z1))) -> c12(A__SEL(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(sel(from(z0), x1)) -> c12(A__SEL(a__from(mark(z0)), mark(x1)), MARK(from(z0))) MARK(sel(first(z0, z1), x1)) -> c12(A__SEL(a__first(mark(z0), mark(z1)), mark(x1)), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), x1)) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), mark(x1)), MARK(sel(z0, z1))) MARK(sel(s(z0), x1)) -> c12(A__SEL(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(sel(x0, s(z0))) -> c12(MARK(x0)) MARK(sel(x0, 0)) -> c12(MARK(x0)) MARK(sel(x0, nil)) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), x1)) -> c12(MARK(cons(z0, z1))) MARK(sel(0, x1)) -> c12(A__SEL(0, mark(x1))) 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c11(MARK(from(x1))) MARK(first(0, from(x1))) -> c11(MARK(from(x1))) MARK(first(nil, from(x1))) -> c11(MARK(from(x1))) MARK(first(x0, first(x1, from(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(first(x1, from(z0)))) MARK(first(x0, first(x1, first(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(first(x1, first(z0, z1)))) MARK(first(x0, first(x1, sel(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(first(x1, sel(z0, z1)))) MARK(first(x0, first(x1, cons(z0, z1)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(first(x1, cons(z0, z1)))) MARK(first(x0, first(x1, s(z0)))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(first(x1, s(z0)))) MARK(first(x0, first(x1, 0))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), 0)), MARK(first(x1, 0))) MARK(first(x0, first(x1, nil))) -> c11(A__FIRST(mark(x0), a__first(mark(x1), nil)), MARK(first(x1, 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-> c12(A__SEL(mark(x0), a__from(nil)), MARK(x0)) MARK(sel(from(z0), from(x1))) -> c12(A__SEL(a__from(mark(z0)), a__from(mark(x1))), MARK(from(z0))) MARK(sel(first(z0, z1), from(x1))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__from(mark(x1))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), from(x1))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__from(mark(x1))), MARK(sel(z0, z1))) MARK(sel(s(z0), from(x1))) -> c12(A__SEL(s(mark(z0)), a__from(mark(x1))), MARK(s(z0))) MARK(sel(x0, from(x1))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), from(x1))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, from(x1))) -> c12(A__SEL(0, a__from(mark(x1)))) MARK(sel(x0, first(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, first(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, first(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__first(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, first(x1, 0))) -> c12(A__SEL(mark(x0), a__first(mark(x1), 0)), MARK(x0)) MARK(sel(x0, first(x1, nil))) -> c12(A__SEL(mark(x0), a__first(mark(x1), nil)), MARK(x0)) MARK(sel(x0, first(from(z0), x2))) -> c12(A__SEL(mark(x0), a__first(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, first(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__first(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, first(s(z0), x2))) -> c12(A__SEL(mark(x0), a__first(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, first(0, x2))) -> c12(A__SEL(mark(x0), a__first(0, mark(x2))), MARK(x0)) MARK(sel(x0, first(nil, x2))) -> c12(A__SEL(mark(x0), a__first(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), first(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__first(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), first(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(first(z0, z1))) MARK(sel(sel(z0, z1), first(x1, x2))) -> c12(A__SEL(a__sel(mark(z0), mark(z1)), a__first(mark(x1), mark(x2))), MARK(sel(z0, z1))) MARK(sel(s(z0), first(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__first(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, first(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), first(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, first(x1, x2))) -> c12(A__SEL(0, a__first(mark(x1), mark(x2)))) MARK(sel(x0, sel(x1, from(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__from(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, first(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__first(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, sel(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), a__sel(mark(z0), mark(z1)))), MARK(x0)) MARK(sel(x0, sel(x1, cons(z0, z1)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(sel(x0, sel(x1, s(z0)))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), s(mark(z0)))), MARK(x0)) MARK(sel(x0, sel(x1, 0))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), 0)), MARK(x0)) MARK(sel(x0, sel(x1, nil))) -> c12(A__SEL(mark(x0), a__sel(mark(x1), nil)), MARK(x0)) MARK(sel(x0, sel(from(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(a__from(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(first(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__first(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(sel(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(a__sel(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(cons(z0, z1), x2))) -> c12(A__SEL(mark(x0), a__sel(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(sel(x0, sel(s(z0), x2))) -> c12(A__SEL(mark(x0), a__sel(s(mark(z0)), mark(x2))), MARK(x0)) MARK(sel(x0, sel(0, x2))) -> c12(A__SEL(mark(x0), a__sel(0, mark(x2))), MARK(x0)) MARK(sel(x0, sel(nil, x2))) -> c12(A__SEL(mark(x0), a__sel(nil, mark(x2))), MARK(x0)) MARK(sel(from(z0), sel(x1, x2))) -> c12(A__SEL(a__from(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(from(z0))) MARK(sel(first(z0, z1), sel(x1, x2))) -> c12(A__SEL(a__first(mark(z0), mark(z1)), a__sel(mark(x1), mark(x2))), MARK(first(z0, z1))) 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(z0, z1))) MARK(sel(s(z0), sel(x1, x2))) -> c12(A__SEL(s(mark(z0)), a__sel(mark(x1), mark(x2))), MARK(s(z0))) MARK(sel(x0, sel(x1, x2))) -> c12(MARK(x0)) MARK(sel(cons(z0, z1), sel(x1, x2))) -> c12(MARK(cons(z0, z1))) MARK(sel(0, sel(x1, x2))) -> c12(A__SEL(0, a__sel(mark(x1), mark(x2)))) K tuples:none Defined Rule Symbols: a__from_1, a__first_2, a__sel_2, mark_1 Defined Pair Symbols: A__FROM_1, A__FIRST_2, A__SEL_2, MARK_1 Compound Symbols: c_1, c3_1, c5_1, c9_2, c14_1, c15_1, c6_1, c7_1, c10_1, c11_1, c12_2, c12_1, c13_2, c13_1, c6_2, c7_2, c10_2, c11_2