KILLED proof of input_L0bz39f3LL.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 45 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 26 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 15.0 s] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 58.0 s] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (24) CpxWeightedTrs (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CpxTypedWeightedTrs (27) CompletionProof [UPPER BOUND(ID), 0 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) InliningProof [UPPER BOUND(ID), 219 ms] (34) CpxRNTS (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRNTS (37) CompletionProof [UPPER BOUND(ID), 0 ms] (38) CpxTypedWeightedCompleteTrs (39) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxRelTRS (49) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (50) CpxTRS (51) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxWeightedTrs (53) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CpxTypedWeightedTrs (55) CompletionProof [UPPER BOUND(ID), 0 ms] (56) CpxTypedWeightedCompleteTrs (57) NarrowingProof [BOTH BOUNDS(ID, ID), 511 ms] (58) CpxTypedWeightedCompleteTrs (59) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) InliningProof [UPPER BOUND(ID), 469 ms] (62) CpxRNTS (63) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CpxRNTS (65) CompletionProof [UPPER BOUND(ID), 0 ms] (66) CpxTypedWeightedCompleteTrs (67) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 6 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (116) CdtProblem (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 10 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (148) CdtProblem (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 100 ms] (150) CdtProblem (151) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 85 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms] (160) CdtProblem (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 148 ms] (162) CdtProblem (163) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 11 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 178 ms] (168) CdtProblem (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 20 ms] (170) CdtProblem (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 33 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 173 ms] (174) CdtProblem (175) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 26 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 42 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 217 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 31 ms] (182) CdtProblem (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (184) CdtProblem (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 213 ms] (186) CdtProblem (187) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 29 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 124 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 93 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 28 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 298 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 73 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 216 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 35 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 138 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 175 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 45 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 144 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 123 ms] (220) CdtProblem (221) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 46 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 237 ms] (224) CdtProblem (225) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 45 ms] (226) CdtProblem (227) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 115 ms] (228) CdtProblem (229) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (230) CdtProblem (231) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 425 ms] (232) CdtProblem (233) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 73 ms] (234) CdtProblem (235) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 231 ms] (236) CdtProblem (237) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 51 ms] (238) CdtProblem (239) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 239 ms] (240) CdtProblem (241) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (242) CdtProblem (243) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 231 ms] (244) CdtProblem (245) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 77 ms] (246) CdtProblem (247) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 254 ms] (248) CdtProblem (249) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 57 ms] (250) CdtProblem (251) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 322 ms] (252) CdtProblem (253) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 97 ms] (254) CdtProblem (255) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 75 ms] (256) CdtProblem (257) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 445 ms] (258) CdtProblem (259) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 75 ms] (260) CdtProblem (261) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 83 ms] (262) 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__pairNs -> cons(0, incr(oddNs)) a__oddNs -> a__incr(a__pairNs) a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) a__take(0, XS) -> nil a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) a__zip(nil, XS) -> nil a__zip(X, nil) -> nil a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) a__tail(cons(X, XS)) -> mark(XS) a__repItems(nil) -> nil a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) mark(pairNs) -> a__pairNs mark(incr(X)) -> a__incr(mark(X)) mark(oddNs) -> a__oddNs mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(repItems(X)) -> a__repItems(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) mark(nil) -> nil mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) a__pairNs -> pairNs a__incr(X) -> incr(X) a__oddNs -> oddNs a__take(X1, X2) -> take(X1, X2) a__zip(X1, X2) -> zip(X1, X2) a__tail(X) -> tail(X) a__repItems(X) -> repItems(X) 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__pairNs -> cons(0', incr(oddNs)) a__oddNs -> a__incr(a__pairNs) a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) a__take(0', XS) -> nil a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) a__zip(nil, XS) -> nil a__zip(X, nil) -> nil a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) a__tail(cons(X, XS)) -> mark(XS) a__repItems(nil) -> nil a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) mark(pairNs) -> a__pairNs mark(incr(X)) -> a__incr(mark(X)) mark(oddNs) -> a__oddNs mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(repItems(X)) -> a__repItems(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0') -> 0' mark(s(X)) -> s(mark(X)) mark(nil) -> nil mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) a__pairNs -> pairNs a__incr(X) -> incr(X) a__oddNs -> oddNs a__take(X1, X2) -> take(X1, X2) a__zip(X1, X2) -> zip(X1, X2) a__tail(X) -> tail(X) a__repItems(X) -> repItems(X) 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__pairNs -> cons(0, incr(oddNs)) a__oddNs -> a__incr(a__pairNs) a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) a__take(0, XS) -> nil a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) a__zip(nil, XS) -> nil a__zip(X, nil) -> nil a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) a__tail(cons(X, XS)) -> mark(XS) a__repItems(nil) -> nil a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) mark(pairNs) -> a__pairNs mark(incr(X)) -> a__incr(mark(X)) mark(oddNs) -> a__oddNs mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) mark(tail(X)) -> a__tail(mark(X)) mark(repItems(X)) -> a__repItems(mark(X)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(s(X)) -> s(mark(X)) mark(nil) -> nil mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) a__pairNs -> pairNs a__incr(X) -> incr(X) a__oddNs -> oddNs a__take(X1, X2) -> take(X1, X2) a__zip(X1, X2) -> zip(X1, X2) a__tail(X) -> tail(X) a__repItems(X) -> repItems(X) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0, z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) S tuples: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0, z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__PAIRNS, A__ODDNS, A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1 Compound Symbols: c, c1, c2_2, c3, c4_1, c5, c6, c7_1, c8, c9, c10, c11_1, c12_1, c13, c14_1, c15, c16, c17_1, c18, c19_1, c20_2, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c29, c30_1, c31, c32_1, c33_1 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0, z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) The (relative) TRS S consists of the following rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0', z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0') -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) The (relative) TRS S consists of the following rules: a__pairNs -> cons(0', incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0', z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0') -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) a__pairNs -> cons(0', incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Types: A__PAIRNS :: c:c1 c :: c:c1 c1 :: c:c1 A__ODDNS :: c2:c3 c2 :: c4:c5 -> c:c1 -> c2:c3 A__INCR :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c4:c5 a__pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c3 :: c2:c3 cons :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c4 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c4:c5 MARK :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c5 :: c4:c5 A__TAKE :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c6:c7:c8 0' :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c6 :: c6:c7:c8 s :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c7 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 A__ZIP :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c9:c10:c11:c12:c13 nil :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c9 :: c9:c10:c11:c12:c13 c10 :: c9:c10:c11:c12:c13 c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c13 :: c9:c10:c11:c12:c13 A__TAIL :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c14:c15 c14 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c14:c15 c15 :: c14:c15 A__REPITEMS :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c16:c17:c18 c16 :: c16:c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18 c18 :: c16:c17:c18 pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c20 :: c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 mark :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c21 :: c2:c3 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c22 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c23 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c24 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c26 :: c14:c15 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c27 :: c16:c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 pair :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c32 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c33 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c:c11_34 :: c:c1 hole_c2:c32_34 :: c2:c3 hole_c4:c53_34 :: c4:c5 hole_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair4_34 :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c335_34 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c9:c10:c11:c12:c137_34 :: c9:c10:c11:c12:c13 hole_c14:c158_34 :: c14:c15 hole_c16:c17:c189_34 :: c16:c17:c18 gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34 :: Nat -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__ODDNS, A__INCR, MARK, A__TAIL, A__REPITEMS, mark, a__oddNs, a__incr, a__tail, a__repItems They will be analysed ascendingly in the following order: A__ODDNS = A__INCR A__ODDNS = MARK A__ODDNS = A__TAIL A__ODDNS = A__REPITEMS A__INCR = MARK A__INCR = A__TAIL A__INCR = A__REPITEMS MARK = A__TAIL MARK = A__REPITEMS mark < MARK A__TAIL = A__REPITEMS mark = a__oddNs mark = a__incr mark = a__tail mark = a__repItems a__oddNs = a__incr a__oddNs = a__tail a__oddNs = a__repItems a__incr = a__tail a__incr = a__repItems a__tail = a__repItems ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0', z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0') -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) a__pairNs -> cons(0', incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Types: A__PAIRNS :: c:c1 c :: c:c1 c1 :: c:c1 A__ODDNS :: c2:c3 c2 :: c4:c5 -> c:c1 -> c2:c3 A__INCR :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c4:c5 a__pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c3 :: c2:c3 cons :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c4 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c4:c5 MARK :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c5 :: c4:c5 A__TAKE :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c6:c7:c8 0' :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c6 :: c6:c7:c8 s :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c7 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 A__ZIP :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c9:c10:c11:c12:c13 nil :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c9 :: c9:c10:c11:c12:c13 c10 :: c9:c10:c11:c12:c13 c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c13 :: c9:c10:c11:c12:c13 A__TAIL :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c14:c15 c14 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c14:c15 c15 :: c14:c15 A__REPITEMS :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c16:c17:c18 c16 :: c16:c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18 c18 :: c16:c17:c18 pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c20 :: c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 mark :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c21 :: c2:c3 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c22 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c23 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c24 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c26 :: c14:c15 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c27 :: c16:c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 pair :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c32 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c33 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c:c11_34 :: c:c1 hole_c2:c32_34 :: c2:c3 hole_c4:c53_34 :: c4:c5 hole_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair4_34 :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c335_34 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c9:c10:c11:c12:c137_34 :: c9:c10:c11:c12:c13 hole_c14:c158_34 :: c14:c15 hole_c16:c17:c189_34 :: c16:c17:c18 gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34 :: Nat -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 Generator Equations: gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(0) <=> 0' gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(x, 1)) <=> cons(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(x), 0') gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c19(c) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c20(c4(c19(c)), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) The following defined symbols remain to be analysed: a__incr, A__ODDNS, A__INCR, MARK, A__TAIL, A__REPITEMS, mark, a__oddNs, a__tail, a__repItems They will be analysed ascendingly in the following order: A__ODDNS = A__INCR A__ODDNS = MARK A__ODDNS = A__TAIL A__ODDNS = A__REPITEMS A__INCR = MARK A__INCR = A__TAIL A__INCR = A__REPITEMS MARK = A__TAIL MARK = A__REPITEMS mark < MARK A__TAIL = A__REPITEMS mark = a__oddNs mark = a__incr mark = a__tail mark = a__repItems a__oddNs = a__incr a__oddNs = a__tail a__oddNs = a__repItems a__incr = a__tail a__incr = a__repItems a__tail = a__repItems ---------------------------------------- (15) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34)) -> gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34), rt in Omega(0) Induction Base: mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(0)) ->_R^Omega(0) 0' Induction Step: mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(n1256788_34, 1))) ->_R^Omega(0) cons(mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34)), 0') ->_IH cons(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(c1256789_34), 0') We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0', z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0') -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) a__pairNs -> cons(0', incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Types: A__PAIRNS :: c:c1 c :: c:c1 c1 :: c:c1 A__ODDNS :: c2:c3 c2 :: c4:c5 -> c:c1 -> c2:c3 A__INCR :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c4:c5 a__pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c3 :: c2:c3 cons :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c4 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c4:c5 MARK :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c5 :: c4:c5 A__TAKE :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c6:c7:c8 0' :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c6 :: c6:c7:c8 s :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c7 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 A__ZIP :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c9:c10:c11:c12:c13 nil :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c9 :: c9:c10:c11:c12:c13 c10 :: c9:c10:c11:c12:c13 c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c13 :: c9:c10:c11:c12:c13 A__TAIL :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c14:c15 c14 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c14:c15 c15 :: c14:c15 A__REPITEMS :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c16:c17:c18 c16 :: c16:c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18 c18 :: c16:c17:c18 pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c20 :: c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 mark :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c21 :: c2:c3 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c22 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c23 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c24 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c26 :: c14:c15 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c27 :: c16:c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 pair :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c32 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c33 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c:c11_34 :: c:c1 hole_c2:c32_34 :: c2:c3 hole_c4:c53_34 :: c4:c5 hole_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair4_34 :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c335_34 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c9:c10:c11:c12:c137_34 :: c9:c10:c11:c12:c13 hole_c14:c158_34 :: c14:c15 hole_c16:c17:c189_34 :: c16:c17:c18 gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34 :: Nat -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 Lemmas: mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34)) -> gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34), rt in Omega(0) Generator Equations: gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(0) <=> 0' gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(x, 1)) <=> cons(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(x), 0') gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c19(c) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c20(c4(c19(c)), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) The following defined symbols remain to be analysed: a__oddNs, A__ODDNS, A__INCR, MARK, A__TAIL, A__REPITEMS, a__incr, a__tail, a__repItems They will be analysed ascendingly in the following order: A__ODDNS = A__INCR A__ODDNS = MARK A__ODDNS = A__TAIL A__ODDNS = A__REPITEMS A__INCR = MARK A__INCR = A__TAIL A__INCR = A__REPITEMS MARK = A__TAIL MARK = A__REPITEMS mark < MARK A__TAIL = A__REPITEMS mark = a__oddNs mark = a__incr mark = a__tail mark = a__repItems a__oddNs = a__incr a__oddNs = a__tail a__oddNs = a__repItems a__incr = a__tail a__incr = a__repItems a__tail = a__repItems ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: MARK(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(1, n10105225_34))) -> *12_34, rt in Omega(n10105225_34) Induction Base: MARK(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(1, 0))) Induction Step: MARK(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(1, +(n10105225_34, 1)))) ->_R^Omega(1) c28(MARK(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(1, n10105225_34)))) ->_IH c28(*12_34) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (18) Complex Obligation (BEST) ---------------------------------------- (19) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0', z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0') -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) a__pairNs -> cons(0', incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Types: A__PAIRNS :: c:c1 c :: c:c1 c1 :: c:c1 A__ODDNS :: c2:c3 c2 :: c4:c5 -> c:c1 -> c2:c3 A__INCR :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c4:c5 a__pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c3 :: c2:c3 cons :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c4 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c4:c5 MARK :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c5 :: c4:c5 A__TAKE :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c6:c7:c8 0' :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c6 :: c6:c7:c8 s :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c7 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 A__ZIP :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c9:c10:c11:c12:c13 nil :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c9 :: c9:c10:c11:c12:c13 c10 :: c9:c10:c11:c12:c13 c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c13 :: c9:c10:c11:c12:c13 A__TAIL :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c14:c15 c14 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c14:c15 c15 :: c14:c15 A__REPITEMS :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c16:c17:c18 c16 :: c16:c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18 c18 :: c16:c17:c18 pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c20 :: c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 mark :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c21 :: c2:c3 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c22 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c23 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c24 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c26 :: c14:c15 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c27 :: c16:c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 pair :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c32 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c33 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c:c11_34 :: c:c1 hole_c2:c32_34 :: c2:c3 hole_c4:c53_34 :: c4:c5 hole_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair4_34 :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c335_34 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c9:c10:c11:c12:c137_34 :: c9:c10:c11:c12:c13 hole_c14:c158_34 :: c14:c15 hole_c16:c17:c189_34 :: c16:c17:c18 gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34 :: Nat -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 Lemmas: mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34)) -> gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34), rt in Omega(0) Generator Equations: gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(0) <=> 0' gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(x, 1)) <=> cons(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(x), 0') gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c19(c) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c20(c4(c19(c)), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) The following defined symbols remain to be analysed: MARK, A__ODDNS, A__TAIL, A__REPITEMS They will be analysed ascendingly in the following order: A__ODDNS = A__INCR A__ODDNS = MARK A__ODDNS = A__TAIL A__ODDNS = A__REPITEMS A__INCR = MARK A__INCR = A__TAIL A__INCR = A__REPITEMS MARK = A__TAIL MARK = A__REPITEMS A__TAIL = A__REPITEMS ---------------------------------------- (20) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (21) BOUNDS(n^1, INF) ---------------------------------------- (22) Obligation: Innermost TRS: Rules: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0', z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0') -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) a__pairNs -> cons(0', incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0', z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0') -> 0' mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Types: A__PAIRNS :: c:c1 c :: c:c1 c1 :: c:c1 A__ODDNS :: c2:c3 c2 :: c4:c5 -> c:c1 -> c2:c3 A__INCR :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c4:c5 a__pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c3 :: c2:c3 cons :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c4 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c4:c5 MARK :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c5 :: c4:c5 A__TAKE :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c6:c7:c8 0' :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c6 :: c6:c7:c8 s :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c7 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c6:c7:c8 c8 :: c6:c7:c8 A__ZIP :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c9:c10:c11:c12:c13 nil :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c9 :: c9:c10:c11:c12:c13 c10 :: c9:c10:c11:c12:c13 c11 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c12 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c9:c10:c11:c12:c13 c13 :: c9:c10:c11:c12:c13 A__TAIL :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c14:c15 c14 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c14:c15 c15 :: c14:c15 A__REPITEMS :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> c16:c17:c18 c16 :: c16:c17:c18 c17 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c16:c17:c18 c18 :: c16:c17:c18 pairNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c19 :: c:c1 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c20 :: c4:c5 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 mark :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c21 :: c2:c3 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c22 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c23 :: c6:c7:c8 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c24 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c25 :: c9:c10:c11:c12:c13 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c26 :: c14:c15 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c27 :: c16:c17:c18 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c28 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c29 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c30 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c31 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 pair :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair c32 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 c33 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 a__oddNs :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__incr :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__take :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__zip :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__tail :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair a__repItems :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c:c11_34 :: c:c1 hole_c2:c32_34 :: c2:c3 hole_c4:c53_34 :: c4:c5 hole_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair4_34 :: cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair hole_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c335_34 :: c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 hole_c6:c7:c86_34 :: c6:c7:c8 hole_c9:c10:c11:c12:c137_34 :: c9:c10:c11:c12:c13 hole_c14:c158_34 :: c14:c15 hole_c16:c17:c189_34 :: c16:c17:c18 gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34 :: Nat -> cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34 :: Nat -> c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33 Lemmas: mark(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34)) -> gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(n1256788_34), rt in Omega(0) MARK(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(1, n10105225_34))) -> *12_34, rt in Omega(n10105225_34) Generator Equations: gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(0) <=> 0' gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(+(x, 1)) <=> cons(gen_cons:0':s:nil:pairNs:incr:oddNs:take:zip:tail:repItems:pair10_34(x), 0') gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(0) <=> c19(c) gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(+(x, 1)) <=> c20(c4(c19(c)), gen_c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c3311_34(x)) The following defined symbols remain to be analysed: A__ODDNS, A__INCR, A__TAIL, A__REPITEMS They will be analysed ascendingly in the following order: A__ODDNS = A__INCR A__ODDNS = MARK A__ODDNS = A__TAIL A__ODDNS = A__REPITEMS A__INCR = MARK A__INCR = A__TAIL A__INCR = A__REPITEMS MARK = A__TAIL MARK = A__REPITEMS A__TAIL = A__REPITEMS ---------------------------------------- (23) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (24) 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__pairNs -> cons(0, incr(oddNs)) [1] a__oddNs -> a__incr(a__pairNs) [1] a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) [1] a__take(0, XS) -> nil [1] a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) [1] a__zip(nil, XS) -> nil [1] a__zip(X, nil) -> nil [1] a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) [1] a__tail(cons(X, XS)) -> mark(XS) [1] a__repItems(nil) -> nil [1] a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) [1] mark(pairNs) -> a__pairNs [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(oddNs) -> a__oddNs [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) [1] mark(tail(X)) -> a__tail(mark(X)) [1] mark(repItems(X)) -> a__repItems(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) [1] a__pairNs -> pairNs [1] a__incr(X) -> incr(X) [1] a__oddNs -> oddNs [1] a__take(X1, X2) -> take(X1, X2) [1] a__zip(X1, X2) -> zip(X1, X2) [1] a__tail(X) -> tail(X) [1] a__repItems(X) -> repItems(X) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (25) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__pairNs -> cons(0, incr(oddNs)) [1] a__oddNs -> a__incr(a__pairNs) [1] a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) [1] a__take(0, XS) -> nil [1] a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) [1] a__zip(nil, XS) -> nil [1] a__zip(X, nil) -> nil [1] a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) [1] a__tail(cons(X, XS)) -> mark(XS) [1] a__repItems(nil) -> nil [1] a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) [1] mark(pairNs) -> a__pairNs [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(oddNs) -> a__oddNs [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) [1] mark(tail(X)) -> a__tail(mark(X)) [1] mark(repItems(X)) -> a__repItems(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) [1] a__pairNs -> pairNs [1] a__incr(X) -> incr(X) [1] a__oddNs -> oddNs [1] a__take(X1, X2) -> take(X1, X2) [1] a__zip(X1, X2) -> zip(X1, X2) [1] a__tail(X) -> tail(X) [1] a__repItems(X) -> repItems(X) [1] The TRS has the following type information: a__pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail cons :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail 0 :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail s :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail mark :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail nil :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pair :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail Rewrite Strategy: INNERMOST ---------------------------------------- (27) 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__pairNs a__tail_1 a__incr_1 a__repItems_1 a__zip_2 a__take_2 a__oddNs Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (28) 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__pairNs -> cons(0, incr(oddNs)) [1] a__oddNs -> a__incr(a__pairNs) [1] a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) [1] a__take(0, XS) -> nil [1] a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) [1] a__zip(nil, XS) -> nil [1] a__zip(X, nil) -> nil [1] a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) [1] a__tail(cons(X, XS)) -> mark(XS) [1] a__repItems(nil) -> nil [1] a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) [1] mark(pairNs) -> a__pairNs [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(oddNs) -> a__oddNs [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) [1] mark(tail(X)) -> a__tail(mark(X)) [1] mark(repItems(X)) -> a__repItems(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) [1] a__pairNs -> pairNs [1] a__incr(X) -> incr(X) [1] a__oddNs -> oddNs [1] a__take(X1, X2) -> take(X1, X2) [1] a__zip(X1, X2) -> zip(X1, X2) [1] a__tail(X) -> tail(X) [1] a__repItems(X) -> repItems(X) [1] The TRS has the following type information: a__pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail cons :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail 0 :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail s :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail mark :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail nil :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pair :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail Rewrite Strategy: INNERMOST ---------------------------------------- (29) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (30) 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__pairNs -> cons(0, incr(oddNs)) [1] a__oddNs -> a__incr(cons(0, incr(oddNs))) [2] a__oddNs -> a__incr(pairNs) [2] a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) [1] a__take(0, XS) -> nil [1] a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) [1] a__zip(nil, XS) -> nil [1] a__zip(X, nil) -> nil [1] a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) [1] a__tail(cons(X, XS)) -> mark(XS) [1] a__repItems(nil) -> nil [1] a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) [1] mark(pairNs) -> a__pairNs [1] mark(incr(pairNs)) -> a__incr(a__pairNs) [2] mark(incr(incr(X'))) -> a__incr(a__incr(mark(X'))) [2] mark(incr(oddNs)) -> a__incr(a__oddNs) [2] mark(incr(take(X1', X2'))) -> a__incr(a__take(mark(X1'), mark(X2'))) [2] mark(incr(zip(X1'', X2''))) -> a__incr(a__zip(mark(X1''), mark(X2''))) [2] mark(incr(tail(X''))) -> a__incr(a__tail(mark(X''))) [2] mark(incr(repItems(X3))) -> a__incr(a__repItems(mark(X3))) [2] mark(incr(cons(X11, X21))) -> a__incr(cons(mark(X11), X21)) [2] mark(incr(0)) -> a__incr(0) [2] mark(incr(s(X4))) -> a__incr(s(mark(X4))) [2] mark(incr(nil)) -> a__incr(nil) [2] mark(incr(pair(X12, X22))) -> a__incr(pair(mark(X12), mark(X22))) [2] mark(oddNs) -> a__oddNs [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) [1] mark(tail(pairNs)) -> a__tail(a__pairNs) [2] mark(tail(incr(X302))) -> a__tail(a__incr(mark(X302))) [2] mark(tail(oddNs)) -> a__tail(a__oddNs) [2] mark(tail(take(X1112, X2107))) -> a__tail(a__take(mark(X1112), mark(X2107))) [2] mark(tail(zip(X1113, X2108))) -> a__tail(a__zip(mark(X1113), mark(X2108))) [2] mark(tail(tail(X303))) -> a__tail(a__tail(mark(X303))) [2] mark(tail(repItems(X304))) -> a__tail(a__repItems(mark(X304))) [2] mark(tail(cons(X1114, X2109))) -> a__tail(cons(mark(X1114), X2109)) [2] mark(tail(0)) -> a__tail(0) [2] mark(tail(s(X305))) -> a__tail(s(mark(X305))) [2] mark(tail(nil)) -> a__tail(nil) [2] mark(tail(pair(X1115, X2110))) -> a__tail(pair(mark(X1115), mark(X2110))) [2] mark(repItems(pairNs)) -> a__repItems(a__pairNs) [2] mark(repItems(incr(X306))) -> a__repItems(a__incr(mark(X306))) [2] mark(repItems(oddNs)) -> a__repItems(a__oddNs) [2] mark(repItems(take(X1116, X2111))) -> a__repItems(a__take(mark(X1116), mark(X2111))) [2] mark(repItems(zip(X1117, X2112))) -> a__repItems(a__zip(mark(X1117), mark(X2112))) [2] mark(repItems(tail(X307))) -> a__repItems(a__tail(mark(X307))) [2] mark(repItems(repItems(X308))) -> a__repItems(a__repItems(mark(X308))) [2] mark(repItems(cons(X1118, X2113))) -> a__repItems(cons(mark(X1118), X2113)) [2] mark(repItems(0)) -> a__repItems(0) [2] mark(repItems(s(X309))) -> a__repItems(s(mark(X309))) [2] mark(repItems(nil)) -> a__repItems(nil) [2] mark(repItems(pair(X1119, X2114))) -> a__repItems(pair(mark(X1119), mark(X2114))) [2] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) [1] a__pairNs -> pairNs [1] a__incr(X) -> incr(X) [1] a__oddNs -> oddNs [1] a__take(X1, X2) -> take(X1, X2) [1] a__zip(X1, X2) -> zip(X1, X2) [1] a__tail(X) -> tail(X) [1] a__repItems(X) -> repItems(X) [1] The TRS has the following type information: a__pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail cons :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail 0 :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail s :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail mark :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail nil :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pair :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail Rewrite Strategy: INNERMOST ---------------------------------------- (31) 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 oddNs => 2 nil => 1 pairNs => 3 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + (1 + mark(X)) + (1 + XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__oddNs -{ 2 }-> a__incr(3) :|: a__oddNs -{ 2 }-> a__incr(1 + 0 + (1 + 2)) :|: a__oddNs -{ 1 }-> 2 :|: a__pairNs -{ 1 }-> 3 :|: a__pairNs -{ 1 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 1 }-> 1 :|: z = 1 a__repItems(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__repItems(z) -{ 1 }-> 1 + mark(X) + (1 + X + (1 + XS)) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> mark(XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> 1 :|: z' = XS, z = 0, XS >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(X) + (1 + N + XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0 a__zip(z, z') -{ 1 }-> 1 :|: z' = XS, z = 1, XS >= 0 a__zip(z, z') -{ 1 }-> 1 :|: X >= 0, z = X, z' = 1 a__zip(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zip(z, z') -{ 1 }-> 1 + (1 + mark(X) + mark(Y)) + (1 + XS + YS) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0 mark(z) -{ 1 }-> a__zip(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__tail(a__zip(mark(X1113), mark(X2108))) :|: z = 1 + (1 + X1113 + X2108), X1113 >= 0, X2108 >= 0 mark(z) -{ 2 }-> a__tail(a__take(mark(X1112), mark(X2107))) :|: z = 1 + (1 + X1112 + X2107), X2107 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__tail(a__tail(mark(X303))) :|: z = 1 + (1 + X303), X303 >= 0 mark(z) -{ 2 }-> a__tail(a__repItems(mark(X304))) :|: z = 1 + (1 + X304), X304 >= 0 mark(z) -{ 2 }-> a__tail(a__pairNs) :|: z = 1 + 3 mark(z) -{ 2 }-> a__tail(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__tail(a__incr(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302) mark(z) -{ 2 }-> a__tail(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__tail(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__tail(1 + mark(X305)) :|: z = 1 + (1 + X305), X305 >= 0 mark(z) -{ 2 }-> a__tail(1 + mark(X1114) + X2109) :|: X1114 >= 0, X2109 >= 0, z = 1 + (1 + X1114 + X2109) mark(z) -{ 2 }-> a__tail(1 + mark(X1115) + mark(X2110)) :|: X1115 >= 0, X2110 >= 0, z = 1 + (1 + X1115 + X2110) mark(z) -{ 2 }-> a__repItems(a__zip(mark(X1117), mark(X2112))) :|: X2112 >= 0, X1117 >= 0, z = 1 + (1 + X1117 + X2112) mark(z) -{ 2 }-> a__repItems(a__take(mark(X1116), mark(X2111))) :|: X1116 >= 0, X2111 >= 0, z = 1 + (1 + X1116 + X2111) mark(z) -{ 2 }-> a__repItems(a__tail(mark(X307))) :|: z = 1 + (1 + X307), X307 >= 0 mark(z) -{ 2 }-> a__repItems(a__repItems(mark(X308))) :|: z = 1 + (1 + X308), X308 >= 0 mark(z) -{ 2 }-> a__repItems(a__pairNs) :|: z = 1 + 3 mark(z) -{ 2 }-> a__repItems(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__repItems(a__incr(mark(X306))) :|: z = 1 + (1 + X306), X306 >= 0 mark(z) -{ 2 }-> a__repItems(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__repItems(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__repItems(1 + mark(X309)) :|: X309 >= 0, z = 1 + (1 + X309) mark(z) -{ 2 }-> a__repItems(1 + mark(X1118) + X2113) :|: z = 1 + (1 + X1118 + X2113), X1118 >= 0, X2113 >= 0 mark(z) -{ 2 }-> a__repItems(1 + mark(X1119) + mark(X2114)) :|: X1119 >= 0, z = 1 + (1 + X1119 + X2114), X2114 >= 0 mark(z) -{ 1 }-> a__pairNs :|: z = 3 mark(z) -{ 1 }-> a__oddNs :|: z = 2 mark(z) -{ 2 }-> a__incr(a__zip(mark(X1''), mark(X2''))) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 mark(z) -{ 2 }-> a__incr(a__take(mark(X1'), mark(X2'))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 mark(z) -{ 2 }-> a__incr(a__tail(mark(X''))) :|: z = 1 + (1 + X''), X'' >= 0 mark(z) -{ 2 }-> a__incr(a__repItems(mark(X3))) :|: z = 1 + (1 + X3), X3 >= 0 mark(z) -{ 2 }-> a__incr(a__pairNs) :|: z = 1 + 3 mark(z) -{ 2 }-> a__incr(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__incr(a__incr(mark(X'))) :|: X' >= 0, z = 1 + (1 + X') mark(z) -{ 2 }-> a__incr(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__incr(1 + mark(X4)) :|: z = 1 + (1 + X4), X4 >= 0 mark(z) -{ 2 }-> a__incr(1 + mark(X11) + X21) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 mark(z) -{ 2 }-> a__incr(1 + mark(X12) + mark(X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) 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 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 ---------------------------------------- (33) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__pairNs -{ 1 }-> 3 :|: a__pairNs -{ 1 }-> 1 + 0 + (1 + 2) :|: ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + (1 + mark(X)) + (1 + XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__oddNs -{ 2 }-> a__incr(3) :|: a__oddNs -{ 2 }-> a__incr(1 + 0 + (1 + 2)) :|: a__oddNs -{ 1 }-> 2 :|: a__pairNs -{ 1 }-> 3 :|: a__pairNs -{ 1 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 1 }-> 1 :|: z = 1 a__repItems(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__repItems(z) -{ 1 }-> 1 + mark(X) + (1 + X + (1 + XS)) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> mark(XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> 1 :|: z' = XS, z = 0, XS >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(X) + (1 + N + XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0 a__zip(z, z') -{ 1 }-> 1 :|: z' = XS, z = 1, XS >= 0 a__zip(z, z') -{ 1 }-> 1 :|: X >= 0, z = X, z' = 1 a__zip(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zip(z, z') -{ 1 }-> 1 + (1 + mark(X) + mark(Y)) + (1 + XS + YS) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0 mark(z) -{ 1 }-> a__zip(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__tail(a__zip(mark(X1113), mark(X2108))) :|: z = 1 + (1 + X1113 + X2108), X1113 >= 0, X2108 >= 0 mark(z) -{ 2 }-> a__tail(a__take(mark(X1112), mark(X2107))) :|: z = 1 + (1 + X1112 + X2107), X2107 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__tail(a__tail(mark(X303))) :|: z = 1 + (1 + X303), X303 >= 0 mark(z) -{ 2 }-> a__tail(a__repItems(mark(X304))) :|: z = 1 + (1 + X304), X304 >= 0 mark(z) -{ 2 }-> a__tail(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__tail(a__incr(mark(X302))) :|: X302 >= 0, z = 1 + (1 + X302) mark(z) -{ 3 }-> a__tail(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__tail(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__tail(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__tail(1 + mark(X305)) :|: z = 1 + (1 + X305), X305 >= 0 mark(z) -{ 2 }-> a__tail(1 + mark(X1114) + X2109) :|: X1114 >= 0, X2109 >= 0, z = 1 + (1 + X1114 + X2109) mark(z) -{ 2 }-> a__tail(1 + mark(X1115) + mark(X2110)) :|: X1115 >= 0, X2110 >= 0, z = 1 + (1 + X1115 + X2110) mark(z) -{ 3 }-> a__tail(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 2 }-> a__repItems(a__zip(mark(X1117), mark(X2112))) :|: X2112 >= 0, X1117 >= 0, z = 1 + (1 + X1117 + X2112) mark(z) -{ 2 }-> a__repItems(a__take(mark(X1116), mark(X2111))) :|: X1116 >= 0, X2111 >= 0, z = 1 + (1 + X1116 + X2111) mark(z) -{ 2 }-> a__repItems(a__tail(mark(X307))) :|: z = 1 + (1 + X307), X307 >= 0 mark(z) -{ 2 }-> a__repItems(a__repItems(mark(X308))) :|: z = 1 + (1 + X308), X308 >= 0 mark(z) -{ 2 }-> a__repItems(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__repItems(a__incr(mark(X306))) :|: z = 1 + (1 + X306), X306 >= 0 mark(z) -{ 3 }-> a__repItems(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__repItems(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__repItems(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__repItems(1 + mark(X309)) :|: X309 >= 0, z = 1 + (1 + X309) mark(z) -{ 2 }-> a__repItems(1 + mark(X1118) + X2113) :|: z = 1 + (1 + X1118 + X2113), X1118 >= 0, X2113 >= 0 mark(z) -{ 2 }-> a__repItems(1 + mark(X1119) + mark(X2114)) :|: X1119 >= 0, z = 1 + (1 + X1119 + X2114), X2114 >= 0 mark(z) -{ 3 }-> a__repItems(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 1 }-> a__oddNs :|: z = 2 mark(z) -{ 2 }-> a__incr(a__zip(mark(X1''), mark(X2''))) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 mark(z) -{ 2 }-> a__incr(a__take(mark(X1'), mark(X2'))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 mark(z) -{ 2 }-> a__incr(a__tail(mark(X''))) :|: z = 1 + (1 + X''), X'' >= 0 mark(z) -{ 2 }-> a__incr(a__repItems(mark(X3))) :|: z = 1 + (1 + X3), X3 >= 0 mark(z) -{ 2 }-> a__incr(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__incr(a__incr(mark(X'))) :|: X' >= 0, z = 1 + (1 + X') mark(z) -{ 3 }-> a__incr(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__incr(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__incr(1 + mark(X4)) :|: z = 1 + (1 + X4), X4 >= 0 mark(z) -{ 2 }-> a__incr(1 + mark(X11) + X21) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 mark(z) -{ 2 }-> a__incr(1 + mark(X12) + mark(X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 3 }-> a__incr(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 2 }-> 3 :|: z = 3 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 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + (1 + 2) :|: z = 3 ---------------------------------------- (35) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a__incr(z) -{ 1 }-> 1 + z :|: z >= 0 a__incr(z) -{ 1 }-> 1 + (1 + mark(X)) + (1 + XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__oddNs -{ 2 }-> a__incr(3) :|: a__oddNs -{ 2 }-> a__incr(1 + 0 + (1 + 2)) :|: a__oddNs -{ 1 }-> 2 :|: a__pairNs -{ 1 }-> 3 :|: a__pairNs -{ 1 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 1 }-> 1 :|: z = 1 a__repItems(z) -{ 1 }-> 1 + z :|: z >= 0 a__repItems(z) -{ 1 }-> 1 + mark(X) + (1 + X + (1 + XS)) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> mark(XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 1 }-> 1 :|: z = 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__take(z, z') -{ 1 }-> 1 + mark(X) + (1 + (z - 1) + XS) :|: z' = 1 + X + XS, X >= 0, XS >= 0, z - 1 >= 0 a__zip(z, z') -{ 1 }-> 1 :|: z = 1, z' >= 0 a__zip(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1 a__zip(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__zip(z, z') -{ 1 }-> 1 + (1 + mark(X) + mark(Y)) + (1 + XS + YS) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0 mark(z) -{ 1 }-> a__zip(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> a__tail(a__zip(mark(X1113), mark(X2108))) :|: z = 1 + (1 + X1113 + X2108), X1113 >= 0, X2108 >= 0 mark(z) -{ 2 }-> a__tail(a__take(mark(X1112), mark(X2107))) :|: z = 1 + (1 + X1112 + X2107), X2107 >= 0, X1112 >= 0 mark(z) -{ 2 }-> a__tail(a__tail(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tail(a__repItems(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tail(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__tail(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__tail(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__tail(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__tail(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__tail(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__tail(1 + mark(X1114) + X2109) :|: X1114 >= 0, X2109 >= 0, z = 1 + (1 + X1114 + X2109) mark(z) -{ 2 }-> a__tail(1 + mark(X1115) + mark(X2110)) :|: X1115 >= 0, X2110 >= 0, z = 1 + (1 + X1115 + X2110) mark(z) -{ 3 }-> a__tail(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 2 }-> a__repItems(a__zip(mark(X1117), mark(X2112))) :|: X2112 >= 0, X1117 >= 0, z = 1 + (1 + X1117 + X2112) mark(z) -{ 2 }-> a__repItems(a__take(mark(X1116), mark(X2111))) :|: X1116 >= 0, X2111 >= 0, z = 1 + (1 + X1116 + X2111) mark(z) -{ 2 }-> a__repItems(a__tail(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__repItems(a__repItems(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__repItems(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__repItems(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__repItems(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__repItems(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__repItems(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__repItems(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__repItems(1 + mark(X1118) + X2113) :|: z = 1 + (1 + X1118 + X2113), X1118 >= 0, X2113 >= 0 mark(z) -{ 2 }-> a__repItems(1 + mark(X1119) + mark(X2114)) :|: X1119 >= 0, z = 1 + (1 + X1119 + X2114), X2114 >= 0 mark(z) -{ 3 }-> a__repItems(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 1 }-> a__oddNs :|: z = 2 mark(z) -{ 2 }-> a__incr(a__zip(mark(X1''), mark(X2''))) :|: X1'' >= 0, z = 1 + (1 + X1'' + X2''), X2'' >= 0 mark(z) -{ 2 }-> a__incr(a__take(mark(X1'), mark(X2'))) :|: z = 1 + (1 + X1' + X2'), X2' >= 0, X1' >= 0 mark(z) -{ 2 }-> a__incr(a__tail(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__incr(a__repItems(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__incr(a__oddNs) :|: z = 1 + 2 mark(z) -{ 2 }-> a__incr(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 3 }-> a__incr(3) :|: z = 1 + 3 mark(z) -{ 2 }-> a__incr(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__incr(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__incr(1 + mark(X11) + X21) :|: z = 1 + (1 + X11 + X21), X11 >= 0, X21 >= 0 mark(z) -{ 2 }-> a__incr(1 + mark(X12) + mark(X22)) :|: X12 >= 0, X22 >= 0, z = 1 + (1 + X12 + X22) mark(z) -{ 3 }-> a__incr(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 2 }-> 3 :|: z = 3 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 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 2 }-> 1 + 0 + (1 + 2) :|: z = 3 ---------------------------------------- (37) 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 ---------------------------------------- (38) 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__pairNs -> cons(0, incr(oddNs)) [1] a__oddNs -> a__incr(a__pairNs) [1] a__incr(cons(X, XS)) -> cons(s(mark(X)), incr(XS)) [1] a__take(0, XS) -> nil [1] a__take(s(N), cons(X, XS)) -> cons(mark(X), take(N, XS)) [1] a__zip(nil, XS) -> nil [1] a__zip(X, nil) -> nil [1] a__zip(cons(X, XS), cons(Y, YS)) -> cons(pair(mark(X), mark(Y)), zip(XS, YS)) [1] a__tail(cons(X, XS)) -> mark(XS) [1] a__repItems(nil) -> nil [1] a__repItems(cons(X, XS)) -> cons(mark(X), cons(X, repItems(XS))) [1] mark(pairNs) -> a__pairNs [1] mark(incr(X)) -> a__incr(mark(X)) [1] mark(oddNs) -> a__oddNs [1] mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) [1] mark(zip(X1, X2)) -> a__zip(mark(X1), mark(X2)) [1] mark(tail(X)) -> a__tail(mark(X)) [1] mark(repItems(X)) -> a__repItems(mark(X)) [1] mark(cons(X1, X2)) -> cons(mark(X1), X2) [1] mark(0) -> 0 [1] mark(s(X)) -> s(mark(X)) [1] mark(nil) -> nil [1] mark(pair(X1, X2)) -> pair(mark(X1), mark(X2)) [1] a__pairNs -> pairNs [1] a__incr(X) -> incr(X) [1] a__oddNs -> oddNs [1] a__take(X1, X2) -> take(X1, X2) [1] a__zip(X1, X2) -> zip(X1, X2) [1] a__tail(X) -> tail(X) [1] a__repItems(X) -> repItems(X) [1] The TRS has the following type information: a__pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail cons :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail 0 :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__oddNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__incr :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail s :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail mark :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail nil :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail take :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pair :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail zip :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail a__repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail repItems :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail pairNs :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail tail :: 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail -> 0:oddNs:incr:cons:s:nil:take:pair:zip:repItems:pairNs:tail Rewrite Strategy: INNERMOST ---------------------------------------- (39) 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 oddNs => 2 nil => 1 pairNs => 3 ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: a__incr(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__incr(z) -{ 1 }-> 1 + (1 + mark(X)) + (1 + XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__oddNs -{ 1 }-> a__incr(a__pairNs) :|: a__oddNs -{ 1 }-> 2 :|: a__pairNs -{ 1 }-> 3 :|: a__pairNs -{ 1 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 1 }-> 1 :|: z = 1 a__repItems(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__repItems(z) -{ 1 }-> 1 + mark(X) + (1 + X + (1 + XS)) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> mark(XS) :|: z = 1 + X + XS, X >= 0, XS >= 0 a__tail(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__take(z, z') -{ 1 }-> 1 :|: z' = XS, z = 0, XS >= 0 a__take(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__take(z, z') -{ 1 }-> 1 + mark(X) + (1 + N + XS) :|: z = 1 + N, z' = 1 + X + XS, X >= 0, XS >= 0, N >= 0 a__zip(z, z') -{ 1 }-> 1 :|: z' = XS, z = 1, XS >= 0 a__zip(z, z') -{ 1 }-> 1 :|: X >= 0, z = X, z' = 1 a__zip(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__zip(z, z') -{ 1 }-> 1 + (1 + mark(X) + mark(Y)) + (1 + XS + YS) :|: z = 1 + X + XS, Y >= 0, X >= 0, YS >= 0, z' = 1 + Y + YS, XS >= 0 mark(z) -{ 1 }-> a__zip(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__take(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__tail(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__repItems(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__pairNs :|: z = 3 mark(z) -{ 1 }-> a__oddNs :|: z = 2 mark(z) -{ 1 }-> a__incr(mark(X)) :|: z = 1 + X, X >= 0 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 mark(z) -{ 1 }-> 1 + mark(X1) + mark(X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (41) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0, z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) S tuples: A__PAIRNS -> c A__PAIRNS -> c1 A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__ODDNS -> c3 A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__INCR(z0) -> c5 A__TAKE(0, z0) -> c6 A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__ZIP(z0, nil) -> c10 A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__ZIP(z0, z1) -> c13 A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__TAIL(z0) -> c15 A__REPITEMS(nil) -> c16 A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) A__REPITEMS(z0) -> c18 MARK(pairNs) -> c19(A__PAIRNS) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(0) -> c29 MARK(s(z0)) -> c30(MARK(z0)) MARK(nil) -> c31 MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__PAIRNS, A__ODDNS, A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1 Compound Symbols: c, c1, c2_2, c3, c4_1, c5, c6, c7_1, c8, c9, c10, c11_1, c12_1, c13, c14_1, c15, c16, c17_1, c18, c19_1, c20_2, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c29, c30_1, c31, c32_1, c33_1 ---------------------------------------- (43) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: MARK(nil) -> c31 A__INCR(z0) -> c5 A__REPITEMS(nil) -> c16 MARK(0) -> c29 A__ODDNS -> c3 A__REPITEMS(z0) -> c18 A__ZIP(z0, nil) -> c10 A__TAKE(z0, z1) -> c8 A__ZIP(nil, z0) -> c9 A__TAKE(0, z0) -> c6 A__TAIL(z0) -> c15 MARK(pairNs) -> c19(A__PAIRNS) A__PAIRNS -> c A__PAIRNS -> c1 A__ZIP(z0, z1) -> c13 ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) S tuples: A__ODDNS -> c2(A__INCR(a__pairNs), A__PAIRNS) A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__ODDNS, A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1 Compound Symbols: c2_2, c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c20_2, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c20_2, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1 ---------------------------------------- (47) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (48) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) The (relative) TRS S consists of the following rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Rewrite Strategy: INNERMOST ---------------------------------------- (49) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (50) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (51) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (52) 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__INCR(cons(z0, z1)) -> c4(MARK(z0)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) [1] A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) [1] A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) [1] MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) [1] MARK(oddNs) -> c21(A__ODDNS) [1] MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) [1] MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) [1] MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) [1] MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c28(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] MARK(pair(z0, z1)) -> c32(MARK(z0)) [1] MARK(pair(z0, z1)) -> c33(MARK(z1)) [1] A__ODDNS -> c2(A__INCR(a__pairNs)) [1] a__pairNs -> cons(0, incr(oddNs)) [0] a__pairNs -> pairNs [0] a__oddNs -> a__incr(a__pairNs) [0] a__oddNs -> oddNs [0] a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [0] a__zip(nil, z0) -> nil [0] a__zip(z0, nil) -> nil [0] a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) [0] a__zip(z0, z1) -> zip(z0, z1) [0] a__tail(cons(z0, z1)) -> mark(z1) [0] a__tail(z0) -> tail(z0) [0] a__repItems(nil) -> nil [0] a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) [0] a__repItems(z0) -> repItems(z0) [0] mark(pairNs) -> a__pairNs [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(oddNs) -> a__oddNs [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) [0] mark(tail(z0)) -> a__tail(mark(z0)) [0] mark(repItems(z0)) -> a__repItems(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (53) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (54) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) [1] A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) [1] A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) [1] MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) [1] MARK(oddNs) -> c21(A__ODDNS) [1] MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) [1] MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) [1] MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) [1] MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c28(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] MARK(pair(z0, z1)) -> c32(MARK(z0)) [1] MARK(pair(z0, z1)) -> c33(MARK(z1)) [1] A__ODDNS -> c2(A__INCR(a__pairNs)) [1] a__pairNs -> cons(0, incr(oddNs)) [0] a__pairNs -> pairNs [0] a__oddNs -> a__incr(a__pairNs) [0] a__oddNs -> oddNs [0] a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [0] a__zip(nil, z0) -> nil [0] a__zip(z0, nil) -> nil [0] a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) [0] a__zip(z0, z1) -> zip(z0, z1) [0] a__tail(cons(z0, z1)) -> mark(z1) [0] a__tail(z0) -> tail(z0) [0] a__repItems(nil) -> nil [0] a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) [0] a__repItems(z0) -> repItems(z0) [0] mark(pairNs) -> a__pairNs [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(oddNs) -> a__oddNs [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) [0] mark(tail(z0)) -> a__tail(mark(z0)) [0] mark(repItems(z0)) -> a__repItems(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) [0] The TRS has the following type information: A__INCR :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> c4 cons :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c4 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c4 MARK :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 A__TAKE :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> c7 s :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c7 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c7 A__ZIP :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> c11:c12 c11 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c11:c12 c12 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c11:c12 A__TAIL :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> c14 c14 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c14 A__REPITEMS :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> c17 c17 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c17 incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c20 :: c4 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c21 :: c2 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 A__ODDNS :: c2 take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c22 :: c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c23 :: c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c24 :: c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c25 :: c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c26 :: c14 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c27 :: c17 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c28 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 pair :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil c32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c33 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c2 :: c4 -> c2 a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil 0 :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil nil :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil Rewrite Strategy: INNERMOST ---------------------------------------- (55) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__INCR_1 A__TAKE_2 A__ZIP_2 A__TAIL_1 A__REPITEMS_1 MARK_1 A__ODDNS (c) The following functions are completely defined: a__pairNs a__oddNs a__incr_1 a__take_2 a__zip_2 a__tail_1 a__repItems_1 mark_1 Due to the following rules being added: a__pairNs -> null_a__pairNs [0] a__oddNs -> null_a__oddNs [0] a__incr(v0) -> null_a__incr [0] a__take(v0, v1) -> null_a__take [0] a__zip(v0, v1) -> null_a__zip [0] a__tail(v0) -> null_a__tail [0] a__repItems(v0) -> null_a__repItems [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__pairNs, null_a__oddNs, null_a__incr, null_a__take, null_a__zip, null_a__tail, null_a__repItems, null_mark, const, const1, const2, const3, const4, const5, const6 ---------------------------------------- (56) 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__INCR(cons(z0, z1)) -> c4(MARK(z0)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) [1] A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) [1] A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) [1] MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) [1] MARK(oddNs) -> c21(A__ODDNS) [1] MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) [1] MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) [1] MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) [1] MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c28(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] MARK(pair(z0, z1)) -> c32(MARK(z0)) [1] MARK(pair(z0, z1)) -> c33(MARK(z1)) [1] A__ODDNS -> c2(A__INCR(a__pairNs)) [1] a__pairNs -> cons(0, incr(oddNs)) [0] a__pairNs -> pairNs [0] a__oddNs -> a__incr(a__pairNs) [0] a__oddNs -> oddNs [0] a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [0] a__zip(nil, z0) -> nil [0] a__zip(z0, nil) -> nil [0] a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) [0] a__zip(z0, z1) -> zip(z0, z1) [0] a__tail(cons(z0, z1)) -> mark(z1) [0] a__tail(z0) -> tail(z0) [0] a__repItems(nil) -> nil [0] a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) [0] a__repItems(z0) -> repItems(z0) [0] mark(pairNs) -> a__pairNs [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(oddNs) -> a__oddNs [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) [0] mark(tail(z0)) -> a__tail(mark(z0)) [0] mark(repItems(z0)) -> a__repItems(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) [0] a__pairNs -> null_a__pairNs [0] a__oddNs -> null_a__oddNs [0] a__incr(v0) -> null_a__incr [0] a__take(v0, v1) -> null_a__take [0] a__zip(v0, v1) -> null_a__zip [0] a__tail(v0) -> null_a__tail [0] a__repItems(v0) -> null_a__repItems [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__INCR :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c4 cons :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c4 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c4 MARK :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 A__TAKE :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c7 s :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c7 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c7 A__ZIP :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c11:c12 c11 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c11:c12 c12 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c11:c12 A__TAIL :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c14 c14 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c14 A__REPITEMS :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c17 c17 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c17 incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c20 :: c4 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c21 :: c2 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 A__ODDNS :: c2 take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c22 :: c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c23 :: c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c24 :: c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c25 :: c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c26 :: c14 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c27 :: c17 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c28 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 pair :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c33 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c2 :: c4 -> c2 a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark 0 :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark nil :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark const :: c4 const1 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 const2 :: c7 const3 :: c11:c12 const4 :: c14 const5 :: c17 const6 :: c2 Rewrite Strategy: INNERMOST ---------------------------------------- (57) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (58) 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__INCR(cons(z0, z1)) -> c4(MARK(z0)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) [1] A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) [1] A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) [1] MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs), MARK(pairNs)) [1] MARK(incr(incr(z0'))) -> c20(A__INCR(a__incr(mark(z0'))), MARK(incr(z0'))) [1] MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) [1] MARK(incr(take(z0'', z1'))) -> c20(A__INCR(a__take(mark(z0''), mark(z1'))), MARK(take(z0'', z1'))) [1] MARK(incr(zip(z01, z1''))) -> c20(A__INCR(a__zip(mark(z01), mark(z1''))), MARK(zip(z01, z1''))) [1] MARK(incr(tail(z02))) -> c20(A__INCR(a__tail(mark(z02))), MARK(tail(z02))) [1] MARK(incr(repItems(z03))) -> c20(A__INCR(a__repItems(mark(z03))), MARK(repItems(z03))) [1] MARK(incr(cons(z04, z11))) -> c20(A__INCR(cons(mark(z04), z11)), MARK(cons(z04, z11))) [1] MARK(incr(0)) -> c20(A__INCR(0), MARK(0)) [1] MARK(incr(s(z05))) -> c20(A__INCR(s(mark(z05))), MARK(s(z05))) [1] MARK(incr(nil)) -> c20(A__INCR(nil), MARK(nil)) [1] MARK(incr(pair(z06, z12))) -> c20(A__INCR(pair(mark(z06), mark(z12))), MARK(pair(z06, z12))) [1] MARK(incr(z0)) -> c20(A__INCR(null_mark), MARK(z0)) [1] MARK(oddNs) -> c21(A__ODDNS) [1] MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) [1] MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) [1] MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs), MARK(pairNs)) [1] MARK(tail(incr(z0455))) -> c26(A__TAIL(a__incr(mark(z0455))), MARK(incr(z0455))) [1] MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) [1] MARK(tail(take(z0456, z1227))) -> c26(A__TAIL(a__take(mark(z0456), mark(z1227))), MARK(take(z0456, z1227))) [1] MARK(tail(zip(z0457, z1228))) -> c26(A__TAIL(a__zip(mark(z0457), mark(z1228))), MARK(zip(z0457, z1228))) [1] MARK(tail(tail(z0458))) -> c26(A__TAIL(a__tail(mark(z0458))), MARK(tail(z0458))) [1] MARK(tail(repItems(z0459))) -> c26(A__TAIL(a__repItems(mark(z0459))), MARK(repItems(z0459))) [1] MARK(tail(cons(z0460, z1229))) -> c26(A__TAIL(cons(mark(z0460), z1229)), MARK(cons(z0460, z1229))) [1] MARK(tail(0)) -> c26(A__TAIL(0), MARK(0)) [1] MARK(tail(s(z0461))) -> c26(A__TAIL(s(mark(z0461))), MARK(s(z0461))) [1] MARK(tail(nil)) -> c26(A__TAIL(nil), MARK(nil)) [1] MARK(tail(pair(z0462, z1230))) -> c26(A__TAIL(pair(mark(z0462), mark(z1230))), MARK(pair(z0462, z1230))) [1] MARK(tail(z0)) -> c26(A__TAIL(null_mark), MARK(z0)) [1] MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs), MARK(pairNs)) [1] MARK(repItems(incr(z0463))) -> c27(A__REPITEMS(a__incr(mark(z0463))), MARK(incr(z0463))) [1] MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) [1] MARK(repItems(take(z0464, z1231))) -> c27(A__REPITEMS(a__take(mark(z0464), mark(z1231))), MARK(take(z0464, z1231))) [1] MARK(repItems(zip(z0465, z1232))) -> c27(A__REPITEMS(a__zip(mark(z0465), mark(z1232))), MARK(zip(z0465, z1232))) [1] MARK(repItems(tail(z0466))) -> c27(A__REPITEMS(a__tail(mark(z0466))), MARK(tail(z0466))) [1] MARK(repItems(repItems(z0467))) -> c27(A__REPITEMS(a__repItems(mark(z0467))), MARK(repItems(z0467))) [1] MARK(repItems(cons(z0468, z1233))) -> c27(A__REPITEMS(cons(mark(z0468), z1233)), MARK(cons(z0468, z1233))) [1] MARK(repItems(0)) -> c27(A__REPITEMS(0), MARK(0)) [1] MARK(repItems(s(z0469))) -> c27(A__REPITEMS(s(mark(z0469))), MARK(s(z0469))) [1] MARK(repItems(nil)) -> c27(A__REPITEMS(nil), MARK(nil)) [1] MARK(repItems(pair(z0470, z1234))) -> c27(A__REPITEMS(pair(mark(z0470), mark(z1234))), MARK(pair(z0470, z1234))) [1] MARK(repItems(z0)) -> c27(A__REPITEMS(null_mark), MARK(z0)) [1] MARK(cons(z0, z1)) -> c28(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] MARK(pair(z0, z1)) -> c32(MARK(z0)) [1] MARK(pair(z0, z1)) -> c33(MARK(z1)) [1] A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) [1] A__ODDNS -> c2(A__INCR(pairNs)) [1] A__ODDNS -> c2(A__INCR(null_a__pairNs)) [1] a__pairNs -> cons(0, incr(oddNs)) [0] a__pairNs -> pairNs [0] a__oddNs -> a__incr(cons(0, incr(oddNs))) [0] a__oddNs -> a__incr(pairNs) [0] a__oddNs -> a__incr(null_a__pairNs) [0] a__oddNs -> oddNs [0] a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [0] a__zip(nil, z0) -> nil [0] a__zip(z0, nil) -> nil [0] a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) [0] a__zip(z0, z1) -> zip(z0, z1) [0] a__tail(cons(z0, z1)) -> mark(z1) [0] a__tail(z0) -> tail(z0) [0] a__repItems(nil) -> nil [0] a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) [0] a__repItems(z0) -> repItems(z0) [0] mark(pairNs) -> a__pairNs [0] mark(incr(pairNs)) -> a__incr(a__pairNs) [0] mark(incr(incr(z0471))) -> a__incr(a__incr(mark(z0471))) [0] mark(incr(oddNs)) -> a__incr(a__oddNs) [0] mark(incr(take(z0472, z1235))) -> a__incr(a__take(mark(z0472), mark(z1235))) [0] mark(incr(zip(z0473, z1236))) -> a__incr(a__zip(mark(z0473), mark(z1236))) [0] mark(incr(tail(z0474))) -> a__incr(a__tail(mark(z0474))) [0] mark(incr(repItems(z0475))) -> a__incr(a__repItems(mark(z0475))) [0] mark(incr(cons(z0476, z1237))) -> a__incr(cons(mark(z0476), z1237)) [0] mark(incr(0)) -> a__incr(0) [0] mark(incr(s(z0477))) -> a__incr(s(mark(z0477))) [0] mark(incr(nil)) -> a__incr(nil) [0] mark(incr(pair(z0478, z1238))) -> a__incr(pair(mark(z0478), mark(z1238))) [0] mark(incr(z0)) -> a__incr(null_mark) [0] mark(oddNs) -> a__oddNs [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) [0] mark(tail(pairNs)) -> a__tail(a__pairNs) [0] mark(tail(incr(z0703))) -> a__tail(a__incr(mark(z0703))) [0] mark(tail(oddNs)) -> a__tail(a__oddNs) [0] mark(tail(take(z0704, z1351))) -> a__tail(a__take(mark(z0704), mark(z1351))) [0] mark(tail(zip(z0705, z1352))) -> a__tail(a__zip(mark(z0705), mark(z1352))) [0] mark(tail(tail(z0706))) -> a__tail(a__tail(mark(z0706))) [0] mark(tail(repItems(z0707))) -> a__tail(a__repItems(mark(z0707))) [0] mark(tail(cons(z0708, z1353))) -> a__tail(cons(mark(z0708), z1353)) [0] mark(tail(0)) -> a__tail(0) [0] mark(tail(s(z0709))) -> a__tail(s(mark(z0709))) [0] mark(tail(nil)) -> a__tail(nil) [0] mark(tail(pair(z0710, z1354))) -> a__tail(pair(mark(z0710), mark(z1354))) [0] mark(tail(z0)) -> a__tail(null_mark) [0] mark(repItems(pairNs)) -> a__repItems(a__pairNs) [0] mark(repItems(incr(z0711))) -> a__repItems(a__incr(mark(z0711))) [0] mark(repItems(oddNs)) -> a__repItems(a__oddNs) [0] mark(repItems(take(z0712, z1355))) -> a__repItems(a__take(mark(z0712), mark(z1355))) [0] mark(repItems(zip(z0713, z1356))) -> a__repItems(a__zip(mark(z0713), mark(z1356))) [0] mark(repItems(tail(z0714))) -> a__repItems(a__tail(mark(z0714))) [0] mark(repItems(repItems(z0715))) -> a__repItems(a__repItems(mark(z0715))) [0] mark(repItems(cons(z0716, z1357))) -> a__repItems(cons(mark(z0716), z1357)) [0] mark(repItems(0)) -> a__repItems(0) [0] mark(repItems(s(z0717))) -> a__repItems(s(mark(z0717))) [0] mark(repItems(nil)) -> a__repItems(nil) [0] mark(repItems(pair(z0718, z1358))) -> a__repItems(pair(mark(z0718), mark(z1358))) [0] mark(repItems(z0)) -> a__repItems(null_mark) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) [0] a__pairNs -> null_a__pairNs [0] a__oddNs -> null_a__oddNs [0] a__incr(v0) -> null_a__incr [0] a__take(v0, v1) -> null_a__take [0] a__zip(v0, v1) -> null_a__zip [0] a__tail(v0) -> null_a__tail [0] a__repItems(v0) -> null_a__repItems [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__INCR :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c4 cons :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c4 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c4 MARK :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 A__TAKE :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c7 s :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c7 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c7 A__ZIP :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c11:c12 c11 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c11:c12 c12 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c11:c12 A__TAIL :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c14 c14 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c14 A__REPITEMS :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c17 c17 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c17 incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c20 :: c4 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c21 :: c2 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 A__ODDNS :: c2 take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c22 :: c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c23 :: c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c24 :: c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c25 :: c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c26 :: c14 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c27 :: c17 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c28 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 pair :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c33 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 c2 :: c4 -> c2 a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark 0 :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark nil :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark const :: c4 const1 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33 const2 :: c7 const3 :: c11:c12 const4 :: c14 const5 :: c17 const6 :: c2 Rewrite Strategy: INNERMOST ---------------------------------------- (59) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: oddNs => 2 0 => 0 pairNs => 3 nil => 1 null_a__pairNs => 0 null_a__oddNs => 0 null_a__incr => 0 null_a__take => 0 null_a__zip => 0 null_a__tail => 0 null_a__repItems => 0 null_mark => 0 const => 0 const1 => 0 const2 => 0 const3 => 0 const4 => 0 const5 => 0 const6 => 0 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: A__INCR(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ODDNS -{ 1 }-> 1 + A__INCR(3) :|: A__ODDNS -{ 1 }-> 1 + A__INCR(0) :|: A__ODDNS -{ 1 }-> 1 + A__INCR(1 + 0 + (1 + 2)) :|: A__REPITEMS(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAIL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ODDNS :|: z = 2 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAIL(a__zip(mark(z0457), mark(z1228))) + MARK(1 + z0457 + z1228) :|: z0457 >= 0, z = 1 + (1 + z0457 + z1228), z1228 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__take(mark(z0456), mark(z1227))) + MARK(1 + z0456 + z1227) :|: z = 1 + (1 + z0456 + z1227), z0456 >= 0, z1227 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__tail(mark(z0458))) + MARK(1 + z0458) :|: z0458 >= 0, z = 1 + (1 + z0458) MARK(z) -{ 1 }-> 1 + A__TAIL(a__repItems(mark(z0459))) + MARK(1 + z0459) :|: z = 1 + (1 + z0459), z0459 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__pairNs) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__TAIL(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TAIL(a__incr(mark(z0455))) + MARK(1 + z0455) :|: z0455 >= 0, z = 1 + (1 + z0455) MARK(z) -{ 1 }-> 1 + A__TAIL(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0461)) + MARK(1 + z0461) :|: z = 1 + (1 + z0461), z0461 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0460) + z1229) + MARK(1 + z0460 + z1229) :|: z = 1 + (1 + z0460 + z1229), z0460 >= 0, z1229 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0462) + mark(z1230)) + MARK(1 + z0462 + z1230) :|: z = 1 + (1 + z0462 + z1230), z1230 >= 0, z0462 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__zip(mark(z0465), mark(z1232))) + MARK(1 + z0465 + z1232) :|: z1232 >= 0, z0465 >= 0, z = 1 + (1 + z0465 + z1232) MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__take(mark(z0464), mark(z1231))) + MARK(1 + z0464 + z1231) :|: z0464 >= 0, z1231 >= 0, z = 1 + (1 + z0464 + z1231) MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__tail(mark(z0466))) + MARK(1 + z0466) :|: z = 1 + (1 + z0466), z0466 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__repItems(mark(z0467))) + MARK(1 + z0467) :|: z = 1 + (1 + z0467), z0467 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__pairNs) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__incr(mark(z0463))) + MARK(1 + z0463) :|: z0463 >= 0, z = 1 + (1 + z0463) MARK(z) -{ 1 }-> 1 + A__REPITEMS(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0469)) + MARK(1 + z0469) :|: z = 1 + (1 + z0469), z0469 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0468) + z1233) + MARK(1 + z0468 + z1233) :|: z1233 >= 0, z0468 >= 0, z = 1 + (1 + z0468 + z1233) MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0470) + mark(z1234)) + MARK(1 + z0470 + z1234) :|: z = 1 + (1 + z0470 + z1234), z0470 >= 0, z1234 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__zip(mark(z01), mark(z1''))) + MARK(1 + z01 + z1'') :|: z = 1 + (1 + z01 + z1''), z01 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__take(mark(z0''), mark(z1'))) + MARK(1 + z0'' + z1') :|: z = 1 + (1 + z0'' + z1'), z1' >= 0, z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__tail(mark(z02))) + MARK(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__repItems(mark(z03))) + MARK(1 + z03) :|: z = 1 + (1 + z03), z03 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__pairNs) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__INCR(a__incr(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z05)) + MARK(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05) MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z04) + z11) + MARK(1 + z04 + z11) :|: z04 >= 0, z = 1 + (1 + z04 + z11), z11 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z06) + mark(z12)) + MARK(1 + z06 + z12) :|: z06 >= 0, z12 >= 0, z = 1 + (1 + z06 + z12) a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 1 + (1 + mark(z0)) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__oddNs -{ 0 }-> a__incr(3) :|: a__oddNs -{ 0 }-> a__incr(0) :|: a__oddNs -{ 0 }-> a__incr(1 + 0 + (1 + 2)) :|: a__oddNs -{ 0 }-> 2 :|: a__oddNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 3 :|: a__pairNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 0 }-> 1 :|: z = 1 a__repItems(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__repItems(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__repItems(z) -{ 0 }-> 1 + mark(z0) + (1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__tail(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__zip(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0 a__zip(z, z') -{ 0 }-> 1 :|: z = z0, z0 >= 0, z' = 1 a__zip(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__zip(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zip(z, z') -{ 0 }-> 1 + (1 + mark(z0) + mark(z2)) + (1 + z1 + z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__zip(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__tail(a__zip(mark(z0705), mark(z1352))) :|: z1352 >= 0, z = 1 + (1 + z0705 + z1352), z0705 >= 0 mark(z) -{ 0 }-> a__tail(a__take(mark(z0704), mark(z1351))) :|: z0704 >= 0, z1351 >= 0, z = 1 + (1 + z0704 + z1351) mark(z) -{ 0 }-> a__tail(a__tail(mark(z0706))) :|: z0706 >= 0, z = 1 + (1 + z0706) mark(z) -{ 0 }-> a__tail(a__repItems(mark(z0707))) :|: z = 1 + (1 + z0707), z0707 >= 0 mark(z) -{ 0 }-> a__tail(a__pairNs) :|: z = 1 + 3 mark(z) -{ 0 }-> a__tail(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tail(a__incr(mark(z0703))) :|: z0703 >= 0, z = 1 + (1 + z0703) mark(z) -{ 0 }-> a__tail(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__tail(1 + mark(z0709)) :|: z0709 >= 0, z = 1 + (1 + z0709) mark(z) -{ 0 }-> a__tail(1 + mark(z0708) + z1353) :|: z1353 >= 0, z0708 >= 0, z = 1 + (1 + z0708 + z1353) mark(z) -{ 0 }-> a__tail(1 + mark(z0710) + mark(z1354)) :|: z0710 >= 0, z1354 >= 0, z = 1 + (1 + z0710 + z1354) mark(z) -{ 0 }-> a__repItems(a__zip(mark(z0713), mark(z1356))) :|: z = 1 + (1 + z0713 + z1356), z0713 >= 0, z1356 >= 0 mark(z) -{ 0 }-> a__repItems(a__take(mark(z0712), mark(z1355))) :|: z = 1 + (1 + z0712 + z1355), z0712 >= 0, z1355 >= 0 mark(z) -{ 0 }-> a__repItems(a__tail(mark(z0714))) :|: z = 1 + (1 + z0714), z0714 >= 0 mark(z) -{ 0 }-> a__repItems(a__repItems(mark(z0715))) :|: z0715 >= 0, z = 1 + (1 + z0715) mark(z) -{ 0 }-> a__repItems(a__pairNs) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__repItems(a__incr(mark(z0711))) :|: z = 1 + (1 + z0711), z0711 >= 0 mark(z) -{ 0 }-> a__repItems(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0717)) :|: z = 1 + (1 + z0717), z0717 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0716) + z1357) :|: z1357 >= 0, z = 1 + (1 + z0716 + z1357), z0716 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0718) + mark(z1358)) :|: z0718 >= 0, z1358 >= 0, z = 1 + (1 + z0718 + z1358) mark(z) -{ 0 }-> a__pairNs :|: z = 3 mark(z) -{ 0 }-> a__oddNs :|: z = 2 mark(z) -{ 0 }-> a__incr(a__zip(mark(z0473), mark(z1236))) :|: z = 1 + (1 + z0473 + z1236), z0473 >= 0, z1236 >= 0 mark(z) -{ 0 }-> a__incr(a__take(mark(z0472), mark(z1235))) :|: z = 1 + (1 + z0472 + z1235), z1235 >= 0, z0472 >= 0 mark(z) -{ 0 }-> a__incr(a__tail(mark(z0474))) :|: z0474 >= 0, z = 1 + (1 + z0474) mark(z) -{ 0 }-> a__incr(a__repItems(mark(z0475))) :|: z0475 >= 0, z = 1 + (1 + z0475) mark(z) -{ 0 }-> a__incr(a__pairNs) :|: z = 1 + 3 mark(z) -{ 0 }-> a__incr(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__incr(a__incr(mark(z0471))) :|: z0471 >= 0, z = 1 + (1 + z0471) mark(z) -{ 0 }-> a__incr(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__incr(1 + mark(z0477)) :|: z = 1 + (1 + z0477), z0477 >= 0 mark(z) -{ 0 }-> a__incr(1 + mark(z0476) + z1237) :|: z1237 >= 0, z0476 >= 0, z = 1 + (1 + z0476 + z1237) mark(z) -{ 0 }-> a__incr(1 + mark(z0478) + mark(z1238)) :|: z0478 >= 0, z = 1 + (1 + z0478 + z1238), z1238 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + mark(z0) + mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 ---------------------------------------- (61) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__pairNs -{ 0 }-> 3 :|: a__pairNs -{ 0 }-> 1 + 0 + (1 + 2) :|: a__pairNs -{ 0 }-> 0 :|: ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: A__INCR(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ODDNS -{ 1 }-> 1 + A__INCR(3) :|: A__ODDNS -{ 1 }-> 1 + A__INCR(0) :|: A__ODDNS -{ 1 }-> 1 + A__INCR(1 + 0 + (1 + 2)) :|: A__REPITEMS(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAIL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ODDNS :|: z = 2 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAIL(a__zip(mark(z0457), mark(z1228))) + MARK(1 + z0457 + z1228) :|: z0457 >= 0, z = 1 + (1 + z0457 + z1228), z1228 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__take(mark(z0456), mark(z1227))) + MARK(1 + z0456 + z1227) :|: z = 1 + (1 + z0456 + z1227), z0456 >= 0, z1227 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__tail(mark(z0458))) + MARK(1 + z0458) :|: z0458 >= 0, z = 1 + (1 + z0458) MARK(z) -{ 1 }-> 1 + A__TAIL(a__repItems(mark(z0459))) + MARK(1 + z0459) :|: z = 1 + (1 + z0459), z0459 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TAIL(a__incr(mark(z0455))) + MARK(1 + z0455) :|: z0455 >= 0, z = 1 + (1 + z0455) MARK(z) -{ 1 }-> 1 + A__TAIL(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__TAIL(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0461)) + MARK(1 + z0461) :|: z = 1 + (1 + z0461), z0461 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0460) + z1229) + MARK(1 + z0460 + z1229) :|: z = 1 + (1 + z0460 + z1229), z0460 >= 0, z1229 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0462) + mark(z1230)) + MARK(1 + z0462 + z1230) :|: z = 1 + (1 + z0462 + z1230), z1230 >= 0, z0462 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + 0 + (1 + 2)) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__zip(mark(z0465), mark(z1232))) + MARK(1 + z0465 + z1232) :|: z1232 >= 0, z0465 >= 0, z = 1 + (1 + z0465 + z1232) MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__take(mark(z0464), mark(z1231))) + MARK(1 + z0464 + z1231) :|: z0464 >= 0, z1231 >= 0, z = 1 + (1 + z0464 + z1231) MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__tail(mark(z0466))) + MARK(1 + z0466) :|: z = 1 + (1 + z0466), z0466 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__repItems(mark(z0467))) + MARK(1 + z0467) :|: z = 1 + (1 + z0467), z0467 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__incr(mark(z0463))) + MARK(1 + z0463) :|: z0463 >= 0, z = 1 + (1 + z0463) MARK(z) -{ 1 }-> 1 + A__REPITEMS(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0469)) + MARK(1 + z0469) :|: z = 1 + (1 + z0469), z0469 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0468) + z1233) + MARK(1 + z0468 + z1233) :|: z1233 >= 0, z0468 >= 0, z = 1 + (1 + z0468 + z1233) MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0470) + mark(z1234)) + MARK(1 + z0470 + z1234) :|: z = 1 + (1 + z0470 + z1234), z0470 >= 0, z1234 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + 0 + (1 + 2)) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(a__zip(mark(z01), mark(z1''))) + MARK(1 + z01 + z1'') :|: z = 1 + (1 + z01 + z1''), z01 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__take(mark(z0''), mark(z1'))) + MARK(1 + z0'' + z1') :|: z = 1 + (1 + z0'' + z1'), z1' >= 0, z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__tail(mark(z02))) + MARK(1 + z02) :|: z = 1 + (1 + z02), z02 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__repItems(mark(z03))) + MARK(1 + z03) :|: z = 1 + (1 + z03), z03 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__INCR(a__incr(mark(z0'))) + MARK(1 + z0') :|: z = 1 + (1 + z0'), z0' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z05)) + MARK(1 + z05) :|: z05 >= 0, z = 1 + (1 + z05) MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z04) + z11) + MARK(1 + z04 + z11) :|: z04 >= 0, z = 1 + (1 + z04 + z11), z11 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z06) + mark(z12)) + MARK(1 + z06 + z12) :|: z06 >= 0, z12 >= 0, z = 1 + (1 + z06 + z12) MARK(z) -{ 1 }-> 1 + A__INCR(1 + 0 + (1 + 2)) + MARK(3) :|: z = 1 + 3 a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 1 + (1 + mark(z0)) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__oddNs -{ 0 }-> a__incr(3) :|: a__oddNs -{ 0 }-> a__incr(0) :|: a__oddNs -{ 0 }-> a__incr(1 + 0 + (1 + 2)) :|: a__oddNs -{ 0 }-> 2 :|: a__oddNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 3 :|: a__pairNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 0 }-> 1 :|: z = 1 a__repItems(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__repItems(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__repItems(z) -{ 0 }-> 1 + mark(z0) + (1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__tail(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__zip(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0 a__zip(z, z') -{ 0 }-> 1 :|: z = z0, z0 >= 0, z' = 1 a__zip(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__zip(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zip(z, z') -{ 0 }-> 1 + (1 + mark(z0) + mark(z2)) + (1 + z1 + z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__zip(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__tail(a__zip(mark(z0705), mark(z1352))) :|: z1352 >= 0, z = 1 + (1 + z0705 + z1352), z0705 >= 0 mark(z) -{ 0 }-> a__tail(a__take(mark(z0704), mark(z1351))) :|: z0704 >= 0, z1351 >= 0, z = 1 + (1 + z0704 + z1351) mark(z) -{ 0 }-> a__tail(a__tail(mark(z0706))) :|: z0706 >= 0, z = 1 + (1 + z0706) mark(z) -{ 0 }-> a__tail(a__repItems(mark(z0707))) :|: z = 1 + (1 + z0707), z0707 >= 0 mark(z) -{ 0 }-> a__tail(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tail(a__incr(mark(z0703))) :|: z0703 >= 0, z = 1 + (1 + z0703) mark(z) -{ 0 }-> a__tail(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__tail(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__tail(1 + mark(z0709)) :|: z0709 >= 0, z = 1 + (1 + z0709) mark(z) -{ 0 }-> a__tail(1 + mark(z0708) + z1353) :|: z1353 >= 0, z0708 >= 0, z = 1 + (1 + z0708 + z1353) mark(z) -{ 0 }-> a__tail(1 + mark(z0710) + mark(z1354)) :|: z0710 >= 0, z1354 >= 0, z = 1 + (1 + z0710 + z1354) mark(z) -{ 0 }-> a__tail(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(a__zip(mark(z0713), mark(z1356))) :|: z = 1 + (1 + z0713 + z1356), z0713 >= 0, z1356 >= 0 mark(z) -{ 0 }-> a__repItems(a__take(mark(z0712), mark(z1355))) :|: z = 1 + (1 + z0712 + z1355), z0712 >= 0, z1355 >= 0 mark(z) -{ 0 }-> a__repItems(a__tail(mark(z0714))) :|: z = 1 + (1 + z0714), z0714 >= 0 mark(z) -{ 0 }-> a__repItems(a__repItems(mark(z0715))) :|: z0715 >= 0, z = 1 + (1 + z0715) mark(z) -{ 0 }-> a__repItems(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__repItems(a__incr(mark(z0711))) :|: z = 1 + (1 + z0711), z0711 >= 0 mark(z) -{ 0 }-> a__repItems(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(1 + mark(z0717)) :|: z = 1 + (1 + z0717), z0717 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0716) + z1357) :|: z1357 >= 0, z = 1 + (1 + z0716 + z1357), z0716 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0718) + mark(z1358)) :|: z0718 >= 0, z1358 >= 0, z = 1 + (1 + z0718 + z1358) mark(z) -{ 0 }-> a__repItems(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 0 }-> a__oddNs :|: z = 2 mark(z) -{ 0 }-> a__incr(a__zip(mark(z0473), mark(z1236))) :|: z = 1 + (1 + z0473 + z1236), z0473 >= 0, z1236 >= 0 mark(z) -{ 0 }-> a__incr(a__take(mark(z0472), mark(z1235))) :|: z = 1 + (1 + z0472 + z1235), z1235 >= 0, z0472 >= 0 mark(z) -{ 0 }-> a__incr(a__tail(mark(z0474))) :|: z0474 >= 0, z = 1 + (1 + z0474) mark(z) -{ 0 }-> a__incr(a__repItems(mark(z0475))) :|: z0475 >= 0, z = 1 + (1 + z0475) mark(z) -{ 0 }-> a__incr(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__incr(a__incr(mark(z0471))) :|: z0471 >= 0, z = 1 + (1 + z0471) mark(z) -{ 0 }-> a__incr(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__incr(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__incr(1 + mark(z0477)) :|: z = 1 + (1 + z0477), z0477 >= 0 mark(z) -{ 0 }-> a__incr(1 + mark(z0476) + z1237) :|: z1237 >= 0, z0476 >= 0, z = 1 + (1 + z0476 + z1237) mark(z) -{ 0 }-> a__incr(1 + mark(z0478) + mark(z1238)) :|: z0478 >= 0, z = 1 + (1 + z0478 + z1238), z1238 >= 0 mark(z) -{ 0 }-> a__incr(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + mark(z0) + mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + (1 + 2) :|: z = 3 ---------------------------------------- (63) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: A__INCR(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ODDNS -{ 1 }-> 1 + A__INCR(3) :|: A__ODDNS -{ 1 }-> 1 + A__INCR(0) :|: A__ODDNS -{ 1 }-> 1 + A__INCR(1 + 0 + (1 + 2)) :|: A__REPITEMS(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAIL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__ODDNS :|: z = 2 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAIL(a__zip(mark(z0457), mark(z1228))) + MARK(1 + z0457 + z1228) :|: z0457 >= 0, z = 1 + (1 + z0457 + z1228), z1228 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__take(mark(z0456), mark(z1227))) + MARK(1 + z0456 + z1227) :|: z = 1 + (1 + z0456 + z1227), z0456 >= 0, z1227 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__tail(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__repItems(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__TAIL(a__incr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__TAIL(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__TAIL(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0460) + z1229) + MARK(1 + z0460 + z1229) :|: z = 1 + (1 + z0460 + z1229), z0460 >= 0, z1229 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + mark(z0462) + mark(z1230)) + MARK(1 + z0462 + z1230) :|: z = 1 + (1 + z0462 + z1230), z1230 >= 0, z0462 >= 0 MARK(z) -{ 1 }-> 1 + A__TAIL(1 + 0 + (1 + 2)) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__zip(mark(z0465), mark(z1232))) + MARK(1 + z0465 + z1232) :|: z1232 >= 0, z0465 >= 0, z = 1 + (1 + z0465 + z1232) MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__take(mark(z0464), mark(z1231))) + MARK(1 + z0464 + z1231) :|: z0464 >= 0, z1231 >= 0, z = 1 + (1 + z0464 + z1231) MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__tail(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__repItems(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__REPITEMS(a__incr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0468) + z1233) + MARK(1 + z0468 + z1233) :|: z1233 >= 0, z0468 >= 0, z = 1 + (1 + z0468 + z1233) MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + mark(z0470) + mark(z1234)) + MARK(1 + z0470 + z1234) :|: z = 1 + (1 + z0470 + z1234), z0470 >= 0, z1234 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(1 + 0 + (1 + 2)) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(a__zip(mark(z01), mark(z1''))) + MARK(1 + z01 + z1'') :|: z = 1 + (1 + z01 + z1''), z01 >= 0, z1'' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__take(mark(z0''), mark(z1'))) + MARK(1 + z0'' + z1') :|: z = 1 + (1 + z0'' + z1'), z1' >= 0, z0'' >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__tail(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__repItems(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(a__oddNs) + MARK(2) :|: z = 1 + 2 MARK(z) -{ 1 }-> 1 + A__INCR(a__incr(mark(z - 2))) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(3) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(1) + MARK(1) :|: z = 1 + 1 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(3) :|: z = 1 + 3 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(0) :|: z = 1 + 0 MARK(z) -{ 1 }-> 1 + A__INCR(0) + MARK(z - 1) :|: z - 1 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z - 2)) + MARK(1 + (z - 2)) :|: z - 2 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z04) + z11) + MARK(1 + z04 + z11) :|: z04 >= 0, z = 1 + (1 + z04 + z11), z11 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(1 + mark(z06) + mark(z12)) + MARK(1 + z06 + z12) :|: z06 >= 0, z12 >= 0, z = 1 + (1 + z06 + z12) MARK(z) -{ 1 }-> 1 + A__INCR(1 + 0 + (1 + 2)) + MARK(3) :|: z = 1 + 3 a__incr(z) -{ 0 }-> 0 :|: z >= 0 a__incr(z) -{ 0 }-> 1 + z :|: z >= 0 a__incr(z) -{ 0 }-> 1 + (1 + mark(z0)) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__oddNs -{ 0 }-> a__incr(3) :|: a__oddNs -{ 0 }-> a__incr(0) :|: a__oddNs -{ 0 }-> a__incr(1 + 0 + (1 + 2)) :|: a__oddNs -{ 0 }-> 2 :|: a__oddNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 3 :|: a__pairNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 0 }-> 1 :|: z = 1 a__repItems(z) -{ 0 }-> 0 :|: z >= 0 a__repItems(z) -{ 0 }-> 1 + z :|: z >= 0 a__repItems(z) -{ 0 }-> 1 + mark(z0) + (1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> 0 :|: z >= 0 a__tail(z) -{ 0 }-> 1 + z :|: z >= 0 a__take(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0 a__take(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__take(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + (z - 1) + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z - 1 >= 0, z2 >= 0 a__zip(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0 a__zip(z, z') -{ 0 }-> 1 :|: z >= 0, z' = 1 a__zip(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 a__zip(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0 a__zip(z, z') -{ 0 }-> 1 + (1 + mark(z0) + mark(z2)) + (1 + z1 + z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__zip(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__tail(a__zip(mark(z0705), mark(z1352))) :|: z1352 >= 0, z = 1 + (1 + z0705 + z1352), z0705 >= 0 mark(z) -{ 0 }-> a__tail(a__take(mark(z0704), mark(z1351))) :|: z0704 >= 0, z1351 >= 0, z = 1 + (1 + z0704 + z1351) mark(z) -{ 0 }-> a__tail(a__tail(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tail(a__repItems(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tail(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__tail(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tail(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__tail(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__tail(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__tail(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__tail(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__tail(1 + mark(z0708) + z1353) :|: z1353 >= 0, z0708 >= 0, z = 1 + (1 + z0708 + z1353) mark(z) -{ 0 }-> a__tail(1 + mark(z0710) + mark(z1354)) :|: z0710 >= 0, z1354 >= 0, z = 1 + (1 + z0710 + z1354) mark(z) -{ 0 }-> a__tail(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(a__zip(mark(z0713), mark(z1356))) :|: z = 1 + (1 + z0713 + z1356), z0713 >= 0, z1356 >= 0 mark(z) -{ 0 }-> a__repItems(a__take(mark(z0712), mark(z1355))) :|: z = 1 + (1 + z0712 + z1355), z0712 >= 0, z1355 >= 0 mark(z) -{ 0 }-> a__repItems(a__tail(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__repItems(a__repItems(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__repItems(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__repItems(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__repItems(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__repItems(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__repItems(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__repItems(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0716) + z1357) :|: z1357 >= 0, z = 1 + (1 + z0716 + z1357), z0716 >= 0 mark(z) -{ 0 }-> a__repItems(1 + mark(z0718) + mark(z1358)) :|: z0718 >= 0, z1358 >= 0, z = 1 + (1 + z0718 + z1358) mark(z) -{ 0 }-> a__repItems(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 0 }-> a__oddNs :|: z = 2 mark(z) -{ 0 }-> a__incr(a__zip(mark(z0473), mark(z1236))) :|: z = 1 + (1 + z0473 + z1236), z0473 >= 0, z1236 >= 0 mark(z) -{ 0 }-> a__incr(a__take(mark(z0472), mark(z1235))) :|: z = 1 + (1 + z0472 + z1235), z1235 >= 0, z0472 >= 0 mark(z) -{ 0 }-> a__incr(a__tail(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(a__repItems(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(a__oddNs) :|: z = 1 + 2 mark(z) -{ 0 }-> a__incr(a__incr(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(3) :|: z = 1 + 3 mark(z) -{ 0 }-> a__incr(1) :|: z = 1 + 1 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + 0 mark(z) -{ 0 }-> a__incr(0) :|: z - 1 >= 0 mark(z) -{ 0 }-> a__incr(0) :|: z = 1 + 3 mark(z) -{ 0 }-> a__incr(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 0 }-> a__incr(1 + mark(z0476) + z1237) :|: z1237 >= 0, z0476 >= 0, z = 1 + (1 + z0476 + z1237) mark(z) -{ 0 }-> a__incr(1 + mark(z0478) + mark(z1238)) :|: z0478 >= 0, z = 1 + (1 + z0478 + z1238), z1238 >= 0 mark(z) -{ 0 }-> a__incr(1 + 0 + (1 + 2)) :|: z = 1 + 3 mark(z) -{ 0 }-> 3 :|: z = 3 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: z >= 0 mark(z) -{ 0 }-> 0 :|: z = 3 mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + mark(z0) + mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + 0 + (1 + 2) :|: z = 3 ---------------------------------------- (65) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__pairNs -> null_a__pairNs [0] a__oddNs -> null_a__oddNs [0] a__incr(v0) -> null_a__incr [0] a__take(v0, v1) -> null_a__take [0] a__zip(v0, v1) -> null_a__zip [0] a__tail(v0) -> null_a__tail [0] a__repItems(v0) -> null_a__repItems [0] mark(v0) -> null_mark [0] A__INCR(v0) -> null_A__INCR [0] A__TAKE(v0, v1) -> null_A__TAKE [0] A__ZIP(v0, v1) -> null_A__ZIP [0] A__TAIL(v0) -> null_A__TAIL [0] A__REPITEMS(v0) -> null_A__REPITEMS [0] MARK(v0) -> null_MARK [0] And the following fresh constants: null_a__pairNs, null_a__oddNs, null_a__incr, null_a__take, null_a__zip, null_a__tail, null_a__repItems, null_mark, null_A__INCR, null_A__TAKE, null_A__ZIP, null_A__TAIL, null_A__REPITEMS, null_MARK, const ---------------------------------------- (66) 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__INCR(cons(z0, z1)) -> c4(MARK(z0)) [1] A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) [1] A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) [1] A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) [1] A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) [1] MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) [1] MARK(oddNs) -> c21(A__ODDNS) [1] MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) [1] MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) [1] MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) [1] MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) [1] MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) [1] MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) [1] MARK(cons(z0, z1)) -> c28(MARK(z0)) [1] MARK(s(z0)) -> c30(MARK(z0)) [1] MARK(pair(z0, z1)) -> c32(MARK(z0)) [1] MARK(pair(z0, z1)) -> c33(MARK(z1)) [1] A__ODDNS -> c2(A__INCR(a__pairNs)) [1] a__pairNs -> cons(0, incr(oddNs)) [0] a__pairNs -> pairNs [0] a__oddNs -> a__incr(a__pairNs) [0] a__oddNs -> oddNs [0] a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) [0] a__incr(z0) -> incr(z0) [0] a__take(0, z0) -> nil [0] a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) [0] a__take(z0, z1) -> take(z0, z1) [0] a__zip(nil, z0) -> nil [0] a__zip(z0, nil) -> nil [0] a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) [0] a__zip(z0, z1) -> zip(z0, z1) [0] a__tail(cons(z0, z1)) -> mark(z1) [0] a__tail(z0) -> tail(z0) [0] a__repItems(nil) -> nil [0] a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) [0] a__repItems(z0) -> repItems(z0) [0] mark(pairNs) -> a__pairNs [0] mark(incr(z0)) -> a__incr(mark(z0)) [0] mark(oddNs) -> a__oddNs [0] mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) [0] mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) [0] mark(tail(z0)) -> a__tail(mark(z0)) [0] mark(repItems(z0)) -> a__repItems(mark(z0)) [0] mark(cons(z0, z1)) -> cons(mark(z0), z1) [0] mark(0) -> 0 [0] mark(s(z0)) -> s(mark(z0)) [0] mark(nil) -> nil [0] mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) [0] a__pairNs -> null_a__pairNs [0] a__oddNs -> null_a__oddNs [0] a__incr(v0) -> null_a__incr [0] a__take(v0, v1) -> null_a__take [0] a__zip(v0, v1) -> null_a__zip [0] a__tail(v0) -> null_a__tail [0] a__repItems(v0) -> null_a__repItems [0] mark(v0) -> null_mark [0] A__INCR(v0) -> null_A__INCR [0] A__TAKE(v0, v1) -> null_A__TAKE [0] A__ZIP(v0, v1) -> null_A__ZIP [0] A__TAIL(v0) -> null_A__TAIL [0] A__REPITEMS(v0) -> null_A__REPITEMS [0] MARK(v0) -> null_MARK [0] The TRS has the following type information: A__INCR :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c4:null_A__INCR cons :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c4 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c4:null_A__INCR MARK :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK A__TAKE :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c7:null_A__TAKE s :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c7 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c7:null_A__TAKE A__ZIP :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c11:c12:null_A__ZIP c11 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c11:c12:null_A__ZIP c12 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c11:c12:null_A__ZIP A__TAIL :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c14:null_A__TAIL c14 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c14:null_A__TAIL A__REPITEMS :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> c17:null_A__REPITEMS c17 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c17:null_A__REPITEMS incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c20 :: c4:null_A__INCR -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c21 :: c2 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK A__ODDNS :: c2 take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c22 :: c7:null_A__TAKE -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK c23 :: c7:null_A__TAKE -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c24 :: c11:c12:null_A__ZIP -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK c25 :: c11:c12:null_A__ZIP -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c26 :: c14:null_A__TAIL -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c27 :: c17:null_A__REPITEMS -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK c28 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK pair :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark c32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK c33 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK c2 :: c4:null_A__INCR -> c2 a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark 0 :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark nil :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark -> cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__pairNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__oddNs :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__incr :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__take :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__zip :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__tail :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_a__repItems :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_mark :: cons:s:incr:oddNs:take:zip:tail:repItems:pair:0:pairNs:nil:null_a__pairNs:null_a__oddNs:null_a__incr:null_a__take:null_a__zip:null_a__tail:null_a__repItems:null_mark null_A__INCR :: c4:null_A__INCR null_A__TAKE :: c7:null_A__TAKE null_A__ZIP :: c11:c12:null_A__ZIP null_A__TAIL :: c14:null_A__TAIL null_A__REPITEMS :: c17:null_A__REPITEMS null_MARK :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c30:c32:c33:null_MARK const :: c2 Rewrite Strategy: INNERMOST ---------------------------------------- (67) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: oddNs => 2 0 => 0 pairNs => 3 nil => 1 null_a__pairNs => 0 null_a__oddNs => 0 null_a__incr => 0 null_a__take => 0 null_a__zip => 0 null_a__tail => 0 null_a__repItems => 0 null_mark => 0 null_A__INCR => 0 null_A__TAKE => 0 null_A__ZIP => 0 null_A__TAIL => 0 null_A__REPITEMS => 0 null_MARK => 0 const => 0 ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: A__INCR(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__INCR(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ODDNS -{ 1 }-> 1 + A__INCR(a__pairNs) :|: A__REPITEMS(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__REPITEMS(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAIL(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__TAIL(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__TAKE(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__TAKE(z, z') -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 A__ZIP(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 A__ZIP(z, z') -{ 1 }-> 1 + MARK(z2) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ODDNS :|: z = 2 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__ZIP(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAKE(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__TAIL(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__REPITEMS(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__INCR(mark(z0)) + MARK(z0) :|: z = 1 + z0, z0 >= 0 a__incr(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__incr(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__incr(z) -{ 0 }-> 1 + (1 + mark(z0)) + (1 + z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__oddNs -{ 0 }-> a__incr(a__pairNs) :|: a__oddNs -{ 0 }-> 2 :|: a__oddNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 3 :|: a__pairNs -{ 0 }-> 0 :|: a__pairNs -{ 0 }-> 1 + 0 + (1 + 2) :|: a__repItems(z) -{ 0 }-> 1 :|: z = 1 a__repItems(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__repItems(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__repItems(z) -{ 0 }-> 1 + mark(z0) + (1 + z0 + (1 + z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__tail(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__tail(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__take(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0 a__take(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__take(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__take(z, z') -{ 0 }-> 1 + mark(z1) + (1 + z0 + z2) :|: z1 >= 0, z' = 1 + z1 + z2, z = 1 + z0, z0 >= 0, z2 >= 0 a__zip(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0 a__zip(z, z') -{ 0 }-> 1 :|: z = z0, z0 >= 0, z' = 1 a__zip(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__zip(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__zip(z, z') -{ 0 }-> 1 + (1 + mark(z0) + mark(z2)) + (1 + z1 + z3) :|: z1 >= 0, z' = 1 + z2 + z3, z0 >= 0, z = 1 + z0 + z1, z2 >= 0, z3 >= 0 mark(z) -{ 0 }-> a__zip(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__take(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__tail(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__repItems(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__pairNs :|: z = 3 mark(z) -{ 0 }-> a__oddNs :|: z = 2 mark(z) -{ 0 }-> a__incr(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> 1 + mark(z0) + z1 :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 + mark(z0) + mark(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (69) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(z0)) -> c20(A__INCR(mark(z0)), MARK(z0)) by MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs), MARK(pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(0)) -> c20(A__INCR(0), MARK(0)) MARK(incr(s(z0))) -> c20(A__INCR(s(mark(z0))), MARK(s(z0))) MARK(incr(nil)) -> c20(A__INCR(nil), MARK(nil)) MARK(incr(pair(z0, z1))) -> c20(A__INCR(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs), MARK(pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(0)) -> c20(A__INCR(0), MARK(0)) MARK(incr(s(z0))) -> c20(A__INCR(s(mark(z0))), MARK(s(z0))) MARK(incr(nil)) -> c20(A__INCR(nil), MARK(nil)) MARK(incr(pair(z0, z1))) -> c20(A__INCR(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs), MARK(pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(0)) -> c20(A__INCR(0), MARK(0)) MARK(incr(s(z0))) -> c20(A__INCR(s(mark(z0))), MARK(s(z0))) MARK(incr(nil)) -> c20(A__INCR(nil), MARK(nil)) MARK(incr(pair(z0, z1))) -> c20(A__INCR(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2 ---------------------------------------- (71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(incr(0)) -> c20(A__INCR(0), MARK(0)) MARK(incr(nil)) -> c20(A__INCR(nil), MARK(nil)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs), MARK(pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(A__INCR(s(mark(z0))), MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(A__INCR(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs), MARK(pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(A__INCR(s(mark(z0))), MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(A__INCR(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c22_2, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c22(A__TAKE(mark(z0), mark(z1)), MARK(z0)) by MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c22(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, s(z0))) -> c22(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c22(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1)), MARK(pairNs)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(cons(z0, z1), x1)) -> c22(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c22(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c22(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(pair(z0, z1), x1)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c22(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, s(z0))) -> c22(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c22(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1)), MARK(pairNs)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(cons(z0, z1), x1)) -> c22(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c22(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c22(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(pair(z0, z1), x1)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c22(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, s(z0))) -> c22(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c22(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1)), MARK(pairNs)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(cons(z0, z1), x1)) -> c22(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(0, x1)) -> c22(A__TAKE(0, mark(x1)), MARK(0)) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(nil, x1)) -> c22(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(pair(z0, z1), x1)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(nil, x1)) -> c22(A__TAKE(nil, mark(x1)), MARK(nil)) MARK(take(0, x1)) -> c22(A__TAKE(0, mark(x1)), MARK(0)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c22(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, s(z0))) -> c22(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c22(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1)), MARK(pairNs)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(cons(z0, z1), x1)) -> c22(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(pair(z0, z1), x1)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(x0, 0)) -> c22(A__TAKE(mark(x0), 0), MARK(x0)) MARK(take(x0, s(z0))) -> c22(A__TAKE(mark(x0), s(mark(z0))), MARK(x0)) MARK(take(x0, nil)) -> c22(A__TAKE(mark(x0), nil), MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1)), MARK(pairNs)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(cons(z0, z1), x1)) -> c22(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(pair(z0, z1), x1)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2 ---------------------------------------- (79) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(z0, z1)) -> c23(A__TAKE(mark(z0), mark(z1)), MARK(z1)) by MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs), MARK(pairNs)) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c23(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, s(z0))) -> c23(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c23(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, pair(z0, z1))) -> c23(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c23(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c23(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c23(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs), MARK(pairNs)) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c23(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, s(z0))) -> c23(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c23(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, pair(z0, z1))) -> c23(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c23(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c23(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c23(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs), MARK(pairNs)) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, 0)) -> c23(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, s(z0))) -> c23(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, nil)) -> c23(A__TAKE(mark(x0), nil), MARK(nil)) MARK(take(x0, pair(z0, z1))) -> c23(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c23(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c23(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c23(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(x0, 0)) -> c23(A__TAKE(mark(x0), 0), MARK(0)) MARK(take(x0, nil)) -> c23(A__TAKE(mark(x0), nil), MARK(nil)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs), MARK(pairNs)) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c23(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c23(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c23(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c23(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs), MARK(pairNs)) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(x0, s(z0))) -> c23(A__TAKE(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(A__TAKE(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(cons(z0, z1), x1)) -> c23(A__TAKE(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(take(0, x1)) -> c23(A__TAKE(0, mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(nil, x1)) -> c23(A__TAKE(nil, mark(x1)), MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c24_2, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1 ---------------------------------------- (87) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(zip(z0, z1)) -> c24(A__ZIP(mark(z0), mark(z1)), MARK(z0)) by MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(x0, 0)) -> c24(A__ZIP(mark(x0), 0), MARK(x0)) MARK(zip(x0, s(z0))) -> c24(A__ZIP(mark(x0), s(mark(z0))), MARK(x0)) MARK(zip(x0, nil)) -> c24(A__ZIP(mark(x0), nil), MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1)), MARK(pairNs)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(0, x1)) -> c24(A__ZIP(0, mark(x1)), MARK(0)) MARK(zip(s(z0), x1)) -> c24(A__ZIP(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(zip(nil, x1)) -> c24(A__ZIP(nil, mark(x1)), MARK(nil)) MARK(zip(pair(z0, z1), x1)) -> c24(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(x0, 0)) -> c24(A__ZIP(mark(x0), 0), MARK(x0)) MARK(zip(x0, s(z0))) -> c24(A__ZIP(mark(x0), s(mark(z0))), MARK(x0)) MARK(zip(x0, nil)) -> c24(A__ZIP(mark(x0), nil), MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1)), MARK(pairNs)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(0, x1)) -> c24(A__ZIP(0, mark(x1)), MARK(0)) MARK(zip(s(z0), x1)) -> c24(A__ZIP(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(zip(nil, x1)) -> c24(A__ZIP(nil, mark(x1)), MARK(nil)) MARK(zip(pair(z0, z1), x1)) -> c24(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(x0, 0)) -> c24(A__ZIP(mark(x0), 0), MARK(x0)) MARK(zip(x0, s(z0))) -> c24(A__ZIP(mark(x0), s(mark(z0))), MARK(x0)) MARK(zip(x0, nil)) -> c24(A__ZIP(mark(x0), nil), MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1)), MARK(pairNs)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(0, x1)) -> c24(A__ZIP(0, mark(x1)), MARK(0)) MARK(zip(s(z0), x1)) -> c24(A__ZIP(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(zip(nil, x1)) -> c24(A__ZIP(nil, mark(x1)), MARK(nil)) MARK(zip(pair(z0, z1), x1)) -> c24(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(zip(nil, x1)) -> c24(A__ZIP(nil, mark(x1)), MARK(nil)) MARK(zip(0, x1)) -> c24(A__ZIP(0, mark(x1)), MARK(0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(x0, 0)) -> c24(A__ZIP(mark(x0), 0), MARK(x0)) MARK(zip(x0, s(z0))) -> c24(A__ZIP(mark(x0), s(mark(z0))), MARK(x0)) MARK(zip(x0, nil)) -> c24(A__ZIP(mark(x0), nil), MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1)), MARK(pairNs)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(s(z0), x1)) -> c24(A__ZIP(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(x0, 0)) -> c24(A__ZIP(mark(x0), 0), MARK(x0)) MARK(zip(x0, s(z0))) -> c24(A__ZIP(mark(x0), s(mark(z0))), MARK(x0)) MARK(zip(x0, nil)) -> c24(A__ZIP(mark(x0), nil), MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1)), MARK(pairNs)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(s(z0), x1)) -> c24(A__ZIP(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c25_2, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(zip(z0, z1)) -> c25(A__ZIP(mark(z0), mark(z1)), MARK(z1)) by MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs), MARK(pairNs)) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c25(A__ZIP(mark(x0), 0), MARK(0)) MARK(zip(x0, s(z0))) -> c25(A__ZIP(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(zip(x0, nil)) -> c25(A__ZIP(mark(x0), nil), MARK(nil)) MARK(zip(x0, pair(z0, z1))) -> c25(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(0, x1)) -> c25(A__ZIP(0, mark(x1)), MARK(x1)) MARK(zip(s(z0), x1)) -> c25(A__ZIP(s(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(nil, x1)) -> c25(A__ZIP(nil, mark(x1)), MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs), MARK(pairNs)) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c25(A__ZIP(mark(x0), 0), MARK(0)) MARK(zip(x0, s(z0))) -> c25(A__ZIP(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(zip(x0, nil)) -> c25(A__ZIP(mark(x0), nil), MARK(nil)) MARK(zip(x0, pair(z0, z1))) -> c25(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(0, x1)) -> c25(A__ZIP(0, mark(x1)), MARK(x1)) MARK(zip(s(z0), x1)) -> c25(A__ZIP(s(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(nil, x1)) -> c25(A__ZIP(nil, mark(x1)), MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs), MARK(pairNs)) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c25(A__ZIP(mark(x0), 0), MARK(0)) MARK(zip(x0, s(z0))) -> c25(A__ZIP(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(zip(x0, nil)) -> c25(A__ZIP(mark(x0), nil), MARK(nil)) MARK(zip(x0, pair(z0, z1))) -> c25(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(0, x1)) -> c25(A__ZIP(0, mark(x1)), MARK(x1)) MARK(zip(s(z0), x1)) -> c25(A__ZIP(s(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(nil, x1)) -> c25(A__ZIP(nil, mark(x1)), MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(zip(x0, 0)) -> c25(A__ZIP(mark(x0), 0), MARK(0)) MARK(zip(x0, nil)) -> c25(A__ZIP(mark(x0), nil), MARK(nil)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs), MARK(pairNs)) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(x0, s(z0))) -> c25(A__ZIP(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(0, x1)) -> c25(A__ZIP(0, mark(x1)), MARK(x1)) MARK(zip(s(z0), x1)) -> c25(A__ZIP(s(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(nil, x1)) -> c25(A__ZIP(nil, mark(x1)), MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs), MARK(pairNs)) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(x0, s(z0))) -> c25(A__ZIP(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(A__ZIP(mark(x0), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(0, x1)) -> c25(A__ZIP(0, mark(x1)), MARK(x1)) MARK(zip(s(z0), x1)) -> c25(A__ZIP(s(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(nil, x1)) -> c25(A__ZIP(nil, mark(x1)), MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(A__ZIP(pair(mark(z0), mark(z1)), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c26_2, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1 ---------------------------------------- (99) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(tail(z0)) -> c26(A__TAIL(mark(z0)), MARK(z0)) by MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs), MARK(pairNs)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(0)) -> c26(A__TAIL(0), MARK(0)) MARK(tail(s(z0))) -> c26(A__TAIL(s(mark(z0))), MARK(s(z0))) MARK(tail(nil)) -> c26(A__TAIL(nil), MARK(nil)) MARK(tail(pair(z0, z1))) -> c26(A__TAIL(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs), MARK(pairNs)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(0)) -> c26(A__TAIL(0), MARK(0)) MARK(tail(s(z0))) -> c26(A__TAIL(s(mark(z0))), MARK(s(z0))) MARK(tail(nil)) -> c26(A__TAIL(nil), MARK(nil)) MARK(tail(pair(z0, z1))) -> c26(A__TAIL(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs), MARK(pairNs)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(0)) -> c26(A__TAIL(0), MARK(0)) MARK(tail(s(z0))) -> c26(A__TAIL(s(mark(z0))), MARK(s(z0))) MARK(tail(nil)) -> c26(A__TAIL(nil), MARK(nil)) MARK(tail(pair(z0, z1))) -> c26(A__TAIL(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(tail(nil)) -> c26(A__TAIL(nil), MARK(nil)) MARK(tail(0)) -> c26(A__TAIL(0), MARK(0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs), MARK(pairNs)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(s(z0))) -> c26(A__TAIL(s(mark(z0))), MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(A__TAIL(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs), MARK(pairNs)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(s(z0))) -> c26(A__TAIL(s(mark(z0))), MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(A__TAIL(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c27_2, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(repItems(z0)) -> c27(A__REPITEMS(mark(z0)), MARK(z0)) by MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs), MARK(pairNs)) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(0)) -> c27(A__REPITEMS(0), MARK(0)) MARK(repItems(s(z0))) -> c27(A__REPITEMS(s(mark(z0))), MARK(s(z0))) MARK(repItems(nil)) -> c27(A__REPITEMS(nil), MARK(nil)) MARK(repItems(pair(z0, z1))) -> c27(A__REPITEMS(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs), MARK(pairNs)) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(0)) -> c27(A__REPITEMS(0), MARK(0)) MARK(repItems(s(z0))) -> c27(A__REPITEMS(s(mark(z0))), MARK(s(z0))) MARK(repItems(nil)) -> c27(A__REPITEMS(nil), MARK(nil)) MARK(repItems(pair(z0, z1))) -> c27(A__REPITEMS(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs), MARK(pairNs)) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(0)) -> c27(A__REPITEMS(0), MARK(0)) MARK(repItems(s(z0))) -> c27(A__REPITEMS(s(mark(z0))), MARK(s(z0))) MARK(repItems(nil)) -> c27(A__REPITEMS(nil), MARK(nil)) MARK(repItems(pair(z0, z1))) -> c27(A__REPITEMS(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(repItems(0)) -> c27(A__REPITEMS(0), MARK(0)) MARK(repItems(nil)) -> c27(A__REPITEMS(nil), MARK(nil)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs), MARK(pairNs)) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(s(z0))) -> c27(A__REPITEMS(s(mark(z0))), MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(A__REPITEMS(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs), MARK(pairNs)) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(s(z0))) -> c27(A__REPITEMS(s(mark(z0))), MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(A__REPITEMS(pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2 ---------------------------------------- (109) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) A__ODDNS -> c2(A__INCR(a__pairNs)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c2_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1 ---------------------------------------- (111) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ODDNS -> c2(A__INCR(a__pairNs)) by A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) A__ODDNS -> c2(A__INCR(pairNs)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) A__ODDNS -> c2(A__INCR(pairNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) A__ODDNS -> c2(A__INCR(pairNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__ODDNS -> c2(A__INCR(pairNs)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(incr(z0))) -> c20(A__INCR(a__incr(mark(z0))), MARK(incr(z0))) by MARK(incr(incr(x0))) -> c20(A__INCR(incr(mark(x0))), MARK(incr(x0))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0)), MARK(incr(0))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil)), MARK(incr(nil))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(x0))) -> c20(A__INCR(incr(mark(x0))), MARK(incr(x0))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0)), MARK(incr(0))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil)), MARK(incr(nil))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(x0))) -> c20(A__INCR(incr(mark(x0))), MARK(incr(x0))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0)), MARK(incr(0))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil)), MARK(incr(nil))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (117) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (119) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(oddNs)) -> c20(A__INCR(a__oddNs), MARK(oddNs)) by MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(A__INCR(oddNs), MARK(oddNs)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(A__INCR(oddNs), MARK(oddNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(A__INCR(oddNs), MARK(oddNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(take(z0, z1))) -> c20(A__INCR(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(incr(take(x0, x1))) -> c20(A__INCR(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, x1))) -> c20(A__INCR(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, x1))) -> c20(A__INCR(take(mark(x0), mark(x1))), MARK(take(x0, x1))) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(zip(z0, z1))) -> c20(A__INCR(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) by MARK(incr(zip(x0, x1))) -> c20(A__INCR(zip(mark(x0), mark(x1))), MARK(zip(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, 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MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, x1))) -> c20(A__INCR(zip(mark(x0), mark(x1))), MARK(zip(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), 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c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(tail(z0))) -> c20(A__INCR(a__tail(mark(z0))), MARK(tail(z0))) by MARK(incr(tail(x0))) -> c20(A__INCR(tail(mark(x0))), MARK(tail(x0))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0)), MARK(tail(0))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil)), MARK(tail(nil))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(x0))) -> c20(A__INCR(tail(mark(x0))), MARK(tail(x0))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0)), MARK(tail(0))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil)), MARK(tail(nil))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(x0))) -> c20(A__INCR(tail(mark(x0))), MARK(tail(x0))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0)), MARK(tail(0))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil)), MARK(tail(nil))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (133) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, 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c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, 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MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> 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c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(repItems(z0))) -> c20(A__INCR(a__repItems(mark(z0))), MARK(repItems(z0))) by MARK(incr(repItems(x0))) -> c20(A__INCR(repItems(mark(x0))), MARK(repItems(x0))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0)), MARK(repItems(0))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil)), MARK(repItems(nil))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(x0))) -> c20(A__INCR(repItems(mark(x0))), MARK(repItems(x0))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0)), MARK(repItems(0))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil)), MARK(repItems(nil))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(x0))) -> c20(A__INCR(repItems(mark(x0))), MARK(repItems(x0))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0)), MARK(repItems(0))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil)), MARK(repItems(nil))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(incr(pairNs)) -> c20(A__INCR(a__pairNs)) by MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(incr(pairNs)) -> c20(A__INCR(pairNs)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(incr(pairNs)) -> c20(A__INCR(pairNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(incr(pairNs)) -> c20(A__INCR(pairNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(incr(pairNs)) -> c20(A__INCR(pairNs)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), a__pairNs), MARK(x0)) by MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), pairNs), MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), pairNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__pairNs), MARK(cons(z0, z1))) MARK(take(0, pairNs)) -> c22(A__TAKE(0, a__pairNs), MARK(0)) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(nil, pairNs)) -> c22(A__TAKE(nil, a__pairNs), MARK(nil)) MARK(take(pair(z0, z1), pairNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__pairNs), MARK(pair(z0, z1))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), pairNs), MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), pairNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__pairNs), MARK(cons(z0, z1))) MARK(take(0, pairNs)) -> c22(A__TAKE(0, a__pairNs), MARK(0)) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(nil, pairNs)) -> c22(A__TAKE(nil, a__pairNs), MARK(nil)) MARK(take(pair(z0, z1), pairNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__pairNs), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), pairNs), MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), pairNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__pairNs), MARK(cons(z0, z1))) MARK(take(0, pairNs)) -> c22(A__TAKE(0, a__pairNs), MARK(0)) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(nil, pairNs)) -> c22(A__TAKE(nil, a__pairNs), MARK(nil)) MARK(take(pair(z0, z1), pairNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__pairNs), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(0, pairNs)) -> c22(A__TAKE(0, a__pairNs), MARK(0)) MARK(take(nil, pairNs)) -> c22(A__TAKE(nil, a__pairNs), MARK(nil)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) 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c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) 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c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), 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c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> 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MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), pairNs), MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), pairNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__pairNs), MARK(cons(z0, z1))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(pair(z0, z1), pairNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__pairNs), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (147) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> 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MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (149) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, incr(z0))) -> c22(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(x0)) by MARK(take(x0, incr(x1))) -> c22(A__TAKE(mark(x0), incr(mark(x1))), MARK(x0)) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), incr(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, incr(x1))) -> c22(A__TAKE(0, a__incr(mark(x1))), MARK(0)) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(nil, incr(x1))) -> c22(A__TAKE(nil, a__incr(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), incr(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(pair(z0, z1))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) 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mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(x1))) -> c22(A__TAKE(mark(x0), incr(mark(x1))), MARK(x0)) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, 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a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), incr(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, incr(x1))) -> c22(A__TAKE(0, a__incr(mark(x1))), MARK(0)) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(nil, incr(x1))) -> c22(A__TAKE(nil, a__incr(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), incr(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> 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c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(x1))) -> c22(A__TAKE(mark(x0), incr(mark(x1))), MARK(x0)) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), incr(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, incr(x1))) -> c22(A__TAKE(0, a__incr(mark(x1))), MARK(0)) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(nil, incr(x1))) -> c22(A__TAKE(nil, a__incr(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), incr(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (151) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(0, incr(x1))) -> c22(A__TAKE(0, a__incr(mark(x1))), MARK(0)) MARK(take(nil, incr(x1))) -> c22(A__TAKE(nil, a__incr(mark(x1))), MARK(nil)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> 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MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(x1))) -> c22(A__TAKE(mark(x0), incr(mark(x1))), MARK(x0)) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), incr(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(pair(z0, z1), incr(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> 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c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__oddNs), MARK(x0)) by MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), oddNs), MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs), MARK(pairNs)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), oddNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(cons(z0, z1))) MARK(take(0, oddNs)) -> c22(A__TAKE(0, a__oddNs), MARK(0)) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(nil, oddNs)) -> c22(A__TAKE(nil, a__oddNs), MARK(nil)) MARK(take(pair(z0, z1), oddNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(pair(z0, z1))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) 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c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) 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c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) 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c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), oddNs), MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs), MARK(pairNs)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), oddNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(cons(z0, z1))) MARK(take(0, oddNs)) -> c22(A__TAKE(0, a__oddNs), MARK(0)) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(nil, oddNs)) -> c22(A__TAKE(nil, a__oddNs), MARK(nil)) MARK(take(pair(z0, z1), oddNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), oddNs), MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs), MARK(pairNs)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), oddNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(cons(z0, z1))) MARK(take(0, oddNs)) -> c22(A__TAKE(0, a__oddNs), MARK(0)) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(nil, oddNs)) -> c22(A__TAKE(nil, a__oddNs), MARK(nil)) MARK(take(pair(z0, z1), oddNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(nil, oddNs)) -> c22(A__TAKE(nil, a__oddNs), MARK(nil)) MARK(take(0, oddNs)) -> c22(A__TAKE(0, a__oddNs), MARK(0)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) 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a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), oddNs), MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs), MARK(pairNs)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), oddNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(cons(z0, z1))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(pair(z0, z1), oddNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), oddNs), MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs), MARK(pairNs)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(cons(z0, z1), oddNs)) -> c22(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(cons(z0, z1))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(pair(z0, z1), oddNs)) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (159) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (161) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, take(z0, z1))) -> c22(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) by MARK(take(x0, take(x1, x2))) -> c22(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(pairNs)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c22(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(nil, take(x1, x2))) -> c22(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(pair(z0, z1))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), 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a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c22(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(nil, take(x1, x2))) -> c22(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, x2))) -> c22(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(pairNs)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, take(x1, x2))) -> c22(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(nil, take(x1, x2))) -> c22(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (163) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(0, take(x1, x2))) -> c22(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(0)) MARK(take(nil, take(x1, x2))) -> c22(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> 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incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, x2))) -> c22(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(pairNs)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), 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MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, 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incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), 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mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, zip(z0, z1))) -> c22(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) by MARK(take(x0, zip(x1, x2))) -> c22(A__TAKE(mark(x0), zip(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(pairNs)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, zip(x1, x2))) -> c22(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(0)) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(nil, zip(x1, x2))) -> c22(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(nil)) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(pair(z0, z1))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) 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MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), 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MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, zip(x1, x2))) -> c22(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(0)) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(nil, zip(x1, x2))) -> c22(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(nil)) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), 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c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, x2))) -> c22(A__TAKE(mark(x0), zip(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(pairNs)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(0, zip(x1, x2))) -> c22(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(0)) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(nil, zip(x1, x2))) -> c22(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(nil)) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(0, zip(x1, x2))) -> c22(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(0)) MARK(take(nil, zip(x1, x2))) -> c22(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(nil)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), 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MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) 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a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, x2))) -> c22(A__TAKE(mark(x0), zip(mark(x1), mark(x2))), MARK(x0)) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(pairNs)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(cons(z0, z1))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (171) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, 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a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> 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MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, tail(z0))) -> c22(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(x0)) by MARK(take(x0, tail(x1))) -> c22(A__TAKE(mark(x0), tail(mark(x1))), MARK(x0)) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), tail(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, tail(x1))) -> c22(A__TAKE(0, a__tail(mark(x1))), MARK(0)) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(nil, tail(x1))) -> c22(A__TAKE(nil, a__tail(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), tail(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(pair(z0, z1))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) 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a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, 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c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(x1))) -> c22(A__TAKE(mark(x0), tail(mark(x1))), MARK(x0)) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), tail(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, tail(x1))) -> c22(A__TAKE(0, a__tail(mark(x1))), MARK(0)) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(nil, tail(x1))) -> c22(A__TAKE(nil, a__tail(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), tail(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) 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MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(x1))) -> c22(A__TAKE(mark(x0), tail(mark(x1))), MARK(x0)) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), tail(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, tail(x1))) -> c22(A__TAKE(0, a__tail(mark(x1))), MARK(0)) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(nil, tail(x1))) -> c22(A__TAKE(nil, a__tail(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), tail(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (175) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(nil, tail(x1))) -> c22(A__TAKE(nil, a__tail(mark(x1))), MARK(nil)) MARK(take(0, tail(x1))) -> c22(A__TAKE(0, a__tail(mark(x1))), MARK(0)) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> 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a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), tail(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(pair(z0, z1), tail(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), 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mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(x1))) -> c22(A__TAKE(mark(x0), tail(mark(x1))), MARK(x0)) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), tail(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(pair(z0, z1), tail(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> 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a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, 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c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> 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MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, 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MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), incr(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), incr(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), incr(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, repItems(z0))) -> c22(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(x0)) by MARK(take(x0, repItems(x1))) -> c22(A__TAKE(mark(x0), repItems(mark(x1))), MARK(x0)) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, repItems(x1))) -> c22(A__TAKE(0, a__repItems(mark(x1))), MARK(0)) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(nil, repItems(x1))) -> c22(A__TAKE(nil, a__repItems(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), repItems(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(pair(z0, z1))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, 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zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(x1))) -> c22(A__TAKE(mark(x0), repItems(mark(x1))), MARK(x0)) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, repItems(x1))) -> c22(A__TAKE(0, a__repItems(mark(x1))), MARK(0)) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(nil, repItems(x1))) -> c22(A__TAKE(nil, a__repItems(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), repItems(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), 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a__incr(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), incr(x1))) -> c22(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(s(z0))) MARK(take(x0, incr(x1))) -> c22(MARK(x0)) MARK(take(pairNs, incr(x1))) -> c22(A__TAKE(a__pairNs, a__incr(mark(x1)))) MARK(take(cons(z0, z1), incr(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), incr(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(incr(z0), oddNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), oddNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(zip(z0, z1))) MARK(take(tail(z0), oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, take(x1, 0))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(x0)) MARK(take(x0, take(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, nil))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(x0)) MARK(take(x0, take(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, take(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(x1))) -> c22(A__TAKE(mark(x0), repItems(mark(x1))), MARK(x0)) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(cons(z0, z1))) MARK(take(0, repItems(x1))) -> c22(A__TAKE(0, a__repItems(mark(x1))), MARK(0)) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(nil, repItems(x1))) -> c22(A__TAKE(nil, a__repItems(mark(x1))), MARK(nil)) MARK(take(pair(z0, z1), repItems(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(nil, repItems(x1))) -> c22(A__TAKE(nil, a__repItems(mark(x1))), MARK(nil)) MARK(take(0, repItems(x1))) -> c22(A__TAKE(0, a__repItems(mark(x1))), MARK(0)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) 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a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(x1))) -> c22(A__TAKE(mark(x0), repItems(mark(x1))), MARK(x0)) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), 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MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(x1))) -> c22(A__TAKE(mark(x0), repItems(mark(x1))), MARK(x0)) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(pairNs)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(cons(z0, z1))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (183) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> 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mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, 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c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, 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zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (185) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, cons(z0, z1))) -> c22(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(x0)) by MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(pairNs)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c22(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(nil, cons(x1, x2))) -> c22(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(pair(z0, z1))) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), 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MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, 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-> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> 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MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(pairNs)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c22(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(nil, cons(x1, x2))) -> c22(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> 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MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(pairNs)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(0, cons(x1, x2))) -> c22(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(nil, cons(x1, x2))) -> c22(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (187) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(0, cons(x1, x2))) -> c22(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) MARK(take(nil, cons(x1, x2))) -> c22(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), 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c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(pairNs)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> 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MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(pairNs)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(z0, z1))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), 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tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) 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oddNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(tail(z0))) MARK(take(repItems(z0), oddNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(repItems(z0))) MARK(take(s(z0), oddNs)) -> c22(A__TAKE(s(mark(z0)), a__oddNs), MARK(s(z0))) MARK(take(x0, oddNs)) -> c22(MARK(x0)) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), oddNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, take(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, take(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, take(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, take(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), 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-> c22(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, take(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, take(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, take(0, x2))) -> c22(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(x0)) MARK(take(x0, take(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, take(nil, x2))) -> c22(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(x0)) MARK(take(x0, take(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), take(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, take(x1, x2))) -> c22(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), take(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), take(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), take(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), take(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, take(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, take(x1, x2))) -> c22(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), take(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), take(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(x1, pairNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(x0)) MARK(take(x0, zip(x1, incr(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, oddNs))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(x0)) MARK(take(x0, zip(x1, take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(x1, tail(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, repItems(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(incr(z0), x1)) -> c22(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) by MARK(take(incr(x0), pairNs)) -> c22(A__TAKE(a__incr(mark(x0)), a__pairNs), MARK(incr(x0))) MARK(take(incr(x0), incr(z0))) -> c22(A__TAKE(a__incr(mark(x0)), a__incr(mark(z0))), MARK(incr(x0))) MARK(take(incr(x0), oddNs)) -> c22(A__TAKE(a__incr(mark(x0)), a__oddNs), MARK(incr(x0))) MARK(take(incr(x0), take(z0, z1))) -> c22(A__TAKE(a__incr(mark(x0)), a__take(mark(z0), mark(z1))), MARK(incr(x0))) MARK(take(incr(x0), zip(z0, z1))) -> c22(A__TAKE(a__incr(mark(x0)), a__zip(mark(z0), mark(z1))), MARK(incr(x0))) MARK(take(incr(x0), tail(z0))) -> c22(A__TAKE(a__incr(mark(x0)), a__tail(mark(z0))), MARK(incr(x0))) MARK(take(incr(x0), repItems(z0))) -> c22(A__TAKE(a__incr(mark(x0)), a__repItems(mark(z0))), MARK(incr(x0))) MARK(take(incr(x0), cons(z0, z1))) -> c22(A__TAKE(a__incr(mark(x0)), cons(mark(z0), z1)), MARK(incr(x0))) MARK(take(incr(x0), 0)) -> c22(A__TAKE(a__incr(mark(x0)), 0), MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(A__TAKE(a__incr(mark(x0)), nil), MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(A__TAKE(incr(mark(x0)), mark(x1)), MARK(incr(x0))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1)), MARK(incr(0))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1)), MARK(incr(nil))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), 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a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(x0), 0)) -> c22(A__TAKE(a__incr(mark(x0)), 0), MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(A__TAKE(a__incr(mark(x0)), nil), MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(A__TAKE(incr(mark(x0)), mark(x1)), MARK(incr(x0))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1)), MARK(incr(0))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1)), MARK(incr(nil))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, 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c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> 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MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, 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MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(x0), 0)) -> c22(A__TAKE(a__incr(mark(x0)), 0), MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(A__TAKE(a__incr(mark(x0)), nil), MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(A__TAKE(incr(mark(x0)), mark(x1)), MARK(incr(x0))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1)), MARK(incr(0))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1)), MARK(incr(nil))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, incr(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, incr(tail(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, incr(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, incr(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, incr(0))) -> c22(A__TAKE(mark(x0), a__incr(0)), MARK(x0)) MARK(take(x0, incr(s(z0)))) -> c22(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(x0)) MARK(take(x0, incr(nil))) -> c22(A__TAKE(mark(x0), a__incr(nil)), MARK(x0)) MARK(take(x0, incr(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), incr(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, incr(x1))) -> c22(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), incr(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), 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-> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), 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MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(oddNs, x1)) -> c22(A__TAKE(a__oddNs, mark(x1)), MARK(oddNs)) by MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(oddNs, incr(z0))) -> c22(A__TAKE(a__oddNs, a__incr(mark(z0))), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c22(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(oddNs, take(z0, z1))) -> c22(A__TAKE(a__oddNs, a__take(mark(z0), mark(z1))), MARK(oddNs)) MARK(take(oddNs, zip(z0, z1))) -> c22(A__TAKE(a__oddNs, a__zip(mark(z0), mark(z1))), MARK(oddNs)) MARK(take(oddNs, tail(z0))) -> c22(A__TAKE(a__oddNs, a__tail(mark(z0))), MARK(oddNs)) MARK(take(oddNs, repItems(z0))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(z0))), MARK(oddNs)) MARK(take(oddNs, cons(z0, z1))) -> c22(A__TAKE(a__oddNs, cons(mark(z0), z1)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(A__TAKE(a__oddNs, 0), MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(A__TAKE(a__oddNs, s(mark(z0))), MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(A__TAKE(a__oddNs, nil), MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(A__TAKE(oddNs, mark(x0)), MARK(oddNs)) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> 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c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, 0)) -> c22(A__TAKE(a__oddNs, 0), MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(A__TAKE(a__oddNs, s(mark(z0))), MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(A__TAKE(a__oddNs, nil), MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(A__TAKE(oddNs, mark(x0)), MARK(oddNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> 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c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), 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z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, 0)) -> c22(A__TAKE(a__oddNs, 0), MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(A__TAKE(a__oddNs, s(mark(z0))), MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(A__TAKE(a__oddNs, nil), MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(A__TAKE(oddNs, mark(x0)), MARK(oddNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) 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c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(tail(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(x0)) MARK(take(x0, zip(0, x2))) -> c22(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(x0)) MARK(take(x0, zip(s(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(nil, x2))) -> c22(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(x0)) MARK(take(x0, zip(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(incr(z0), zip(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(incr(z0))) MARK(take(oddNs, zip(x1, x2))) -> c22(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(oddNs)) MARK(take(take(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) 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MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, 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MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(take(z0, z1), x1)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) by MARK(take(take(x0, x1), pairNs)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__pairNs), MARK(take(x0, x1))) MARK(take(take(x0, x1), incr(z0))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__incr(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), oddNs)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__oddNs), MARK(take(x0, x1))) MARK(take(take(x0, x1), take(z0, z1))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__take(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), zip(z0, z1))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__zip(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), tail(z0))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__tail(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), repItems(z0))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), a__repItems(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), cons(z0, z1))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(take(x0, x1))) MARK(take(take(x0, x1), 0)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), pair(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) 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c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, x1), 0)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), pair(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) 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-> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, x1), 0)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), 0), MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), s(mark(z0))), MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), nil), MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(A__TAKE(a__take(mark(x0), mark(x1)), pair(mark(z0), mark(z1))), MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(A__TAKE(take(mark(x0), mark(x1)), mark(x2)), MARK(take(x0, x1))) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(incr(tail(x0))) -> c20(MARK(tail(x0))) MARK(incr(tail(0))) -> c20(A__INCR(a__tail(0))) MARK(incr(tail(nil))) -> c20(A__INCR(a__tail(nil))) MARK(incr(repItems(pairNs))) -> c20(A__INCR(a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(incr(repItems(incr(z0)))) -> c20(A__INCR(a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(incr(repItems(oddNs))) -> c20(A__INCR(a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(incr(repItems(take(z0, z1)))) -> c20(A__INCR(a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(incr(repItems(zip(z0, z1)))) -> c20(A__INCR(a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(incr(repItems(tail(z0)))) -> c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) 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MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) 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MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(zip(z0, z1), x1)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) by MARK(take(zip(x0, x1), pairNs)) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__pairNs), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), incr(z0))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__incr(mark(z0))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), oddNs)) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__oddNs), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), take(z0, z1))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__take(mark(z0), mark(z1))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), zip(z0, z1))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__zip(mark(z0), mark(z1))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), tail(z0))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__tail(mark(z0))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), repItems(z0))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), a__repItems(mark(z0))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), cons(z0, z1))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), cons(mark(z0), z1)), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), 0)) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), 0), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), s(mark(z0))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), nil), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), pair(mark(z0), mark(z1))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(A__TAKE(zip(mark(x0), mark(x1)), mark(x2)), MARK(zip(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> 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a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, x1), 0)) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), 0), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), s(mark(z0))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), nil), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(A__TAKE(a__zip(mark(x0), mark(x1)), pair(mark(z0), mark(z1))), MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(A__TAKE(zip(mark(x0), mark(x1)), mark(x2)), MARK(zip(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) 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MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) 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a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, 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MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) 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MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(tail(z0), x1)) -> c22(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) by MARK(take(tail(x0), pairNs)) -> c22(A__TAKE(a__tail(mark(x0)), a__pairNs), MARK(tail(x0))) MARK(take(tail(x0), incr(z0))) -> c22(A__TAKE(a__tail(mark(x0)), a__incr(mark(z0))), MARK(tail(x0))) MARK(take(tail(x0), oddNs)) -> c22(A__TAKE(a__tail(mark(x0)), a__oddNs), MARK(tail(x0))) MARK(take(tail(x0), take(z0, z1))) -> c22(A__TAKE(a__tail(mark(x0)), a__take(mark(z0), mark(z1))), MARK(tail(x0))) MARK(take(tail(x0), zip(z0, z1))) -> c22(A__TAKE(a__tail(mark(x0)), a__zip(mark(z0), mark(z1))), MARK(tail(x0))) MARK(take(tail(x0), tail(z0))) -> c22(A__TAKE(a__tail(mark(x0)), a__tail(mark(z0))), MARK(tail(x0))) MARK(take(tail(x0), repItems(z0))) -> c22(A__TAKE(a__tail(mark(x0)), a__repItems(mark(z0))), MARK(tail(x0))) MARK(take(tail(x0), cons(z0, z1))) -> c22(A__TAKE(a__tail(mark(x0)), cons(mark(z0), z1)), MARK(tail(x0))) MARK(take(tail(x0), 0)) -> c22(A__TAKE(a__tail(mark(x0)), 0), MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(A__TAKE(a__tail(mark(x0)), s(mark(z0))), MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(A__TAKE(a__tail(mark(x0)), nil), MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(A__TAKE(a__tail(mark(x0)), pair(mark(z0), mark(z1))), MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(A__TAKE(tail(mark(x0)), mark(x1)), MARK(tail(x0))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1)), MARK(tail(0))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1)), MARK(tail(nil))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> 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mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(x0), 0)) -> c22(A__TAKE(a__tail(mark(x0)), 0), MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(A__TAKE(a__tail(mark(x0)), s(mark(z0))), MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(A__TAKE(a__tail(mark(x0)), nil), MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(A__TAKE(a__tail(mark(x0)), pair(mark(z0), mark(z1))), MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(A__TAKE(tail(mark(x0)), mark(x1)), MARK(tail(x0))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1)), MARK(tail(0))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1)), MARK(tail(nil))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> 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c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), 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z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(x0), 0)) -> c22(A__TAKE(a__tail(mark(x0)), 0), MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(A__TAKE(a__tail(mark(x0)), s(mark(z0))), MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(A__TAKE(a__tail(mark(x0)), nil), MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(A__TAKE(a__tail(mark(x0)), pair(mark(z0), mark(z1))), MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(A__TAKE(tail(mark(x0)), mark(x1)), MARK(tail(x0))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1)), MARK(tail(0))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1)), MARK(tail(nil))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), 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c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> 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c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(repItems(z0), x1)) -> c22(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) by MARK(take(repItems(x0), pairNs)) -> c22(A__TAKE(a__repItems(mark(x0)), a__pairNs), MARK(repItems(x0))) MARK(take(repItems(x0), incr(z0))) -> c22(A__TAKE(a__repItems(mark(x0)), a__incr(mark(z0))), MARK(repItems(x0))) MARK(take(repItems(x0), oddNs)) -> c22(A__TAKE(a__repItems(mark(x0)), a__oddNs), MARK(repItems(x0))) MARK(take(repItems(x0), take(z0, z1))) -> c22(A__TAKE(a__repItems(mark(x0)), a__take(mark(z0), mark(z1))), MARK(repItems(x0))) MARK(take(repItems(x0), zip(z0, z1))) -> c22(A__TAKE(a__repItems(mark(x0)), a__zip(mark(z0), mark(z1))), MARK(repItems(x0))) MARK(take(repItems(x0), tail(z0))) -> c22(A__TAKE(a__repItems(mark(x0)), a__tail(mark(z0))), MARK(repItems(x0))) MARK(take(repItems(x0), repItems(z0))) -> c22(A__TAKE(a__repItems(mark(x0)), a__repItems(mark(z0))), MARK(repItems(x0))) MARK(take(repItems(x0), cons(z0, z1))) -> c22(A__TAKE(a__repItems(mark(x0)), cons(mark(z0), z1)), MARK(repItems(x0))) MARK(take(repItems(x0), 0)) -> c22(A__TAKE(a__repItems(mark(x0)), 0), MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(A__TAKE(a__repItems(mark(x0)), s(mark(z0))), MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(A__TAKE(a__repItems(mark(x0)), nil), MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(A__TAKE(a__repItems(mark(x0)), pair(mark(z0), mark(z1))), MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(A__TAKE(repItems(mark(x0)), mark(x1)), MARK(repItems(x0))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1)), MARK(repItems(0))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1)), MARK(repItems(nil))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> 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a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, 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a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(x0), 0)) -> c22(A__TAKE(a__repItems(mark(x0)), 0), MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(A__TAKE(a__repItems(mark(x0)), s(mark(z0))), MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(A__TAKE(a__repItems(mark(x0)), nil), MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(A__TAKE(a__repItems(mark(x0)), pair(mark(z0), mark(z1))), MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(A__TAKE(repItems(mark(x0)), mark(x1)), MARK(repItems(x0))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1)), MARK(repItems(0))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1)), MARK(repItems(nil))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, 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c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, 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MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(x0), 0)) -> c22(A__TAKE(a__repItems(mark(x0)), 0), MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(A__TAKE(a__repItems(mark(x0)), s(mark(z0))), MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(A__TAKE(a__repItems(mark(x0)), nil), MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(A__TAKE(a__repItems(mark(x0)), pair(mark(z0), mark(z1))), MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(A__TAKE(repItems(mark(x0)), mark(x1)), MARK(repItems(x0))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1)), MARK(repItems(0))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1)), MARK(repItems(nil))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) 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MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), 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c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_2, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(s(z0), x1)) -> c22(A__TAKE(s(mark(z0)), mark(x1)), MARK(s(z0))) by MARK(take(s(x0), pairNs)) -> c22(A__TAKE(s(mark(x0)), a__pairNs), MARK(s(x0))) MARK(take(s(x0), incr(z0))) -> c22(A__TAKE(s(mark(x0)), a__incr(mark(z0))), MARK(s(x0))) MARK(take(s(x0), oddNs)) -> c22(A__TAKE(s(mark(x0)), a__oddNs), MARK(s(x0))) MARK(take(s(x0), take(z0, z1))) -> c22(A__TAKE(s(mark(x0)), a__take(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(x0), zip(z0, z1))) -> c22(A__TAKE(s(mark(x0)), a__zip(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(x0), tail(z0))) -> c22(A__TAKE(s(mark(x0)), a__tail(mark(z0))), MARK(s(x0))) MARK(take(s(x0), repItems(z0))) -> c22(A__TAKE(s(mark(x0)), a__repItems(mark(z0))), MARK(s(x0))) MARK(take(s(x0), cons(z0, z1))) -> c22(A__TAKE(s(mark(x0)), cons(mark(z0), z1)), MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(A__TAKE(s(mark(x0)), pair(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> 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c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(x0), 0)) -> c22(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(A__TAKE(s(mark(x0)), pair(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), 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oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(x0), 0)) -> c22(A__TAKE(s(mark(x0)), 0), MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(A__TAKE(s(mark(x0)), s(mark(z0))), MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(A__TAKE(s(mark(x0)), nil), MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(A__TAKE(s(mark(x0)), pair(mark(z0), mark(z1))), MARK(s(x0))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), 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c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) 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c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, 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MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(pairNs, x1)) -> c22(A__TAKE(a__pairNs, mark(x1))) by MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(pairNs, incr(z0))) -> c22(A__TAKE(a__pairNs, a__incr(mark(z0)))) MARK(take(pairNs, oddNs)) -> c22(A__TAKE(a__pairNs, a__oddNs)) MARK(take(pairNs, take(z0, z1))) -> c22(A__TAKE(a__pairNs, a__take(mark(z0), mark(z1)))) MARK(take(pairNs, zip(z0, z1))) -> c22(A__TAKE(a__pairNs, a__zip(mark(z0), mark(z1)))) MARK(take(pairNs, tail(z0))) -> c22(A__TAKE(a__pairNs, a__tail(mark(z0)))) MARK(take(pairNs, repItems(z0))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(z0)))) MARK(take(pairNs, cons(z0, z1))) -> c22(A__TAKE(a__pairNs, cons(mark(z0), z1))) MARK(take(pairNs, 0)) -> c22(A__TAKE(a__pairNs, 0)) MARK(take(pairNs, s(z0))) -> c22(A__TAKE(a__pairNs, s(mark(z0)))) MARK(take(pairNs, nil)) -> c22(A__TAKE(a__pairNs, nil)) MARK(take(pairNs, pair(z0, z1))) -> c22(A__TAKE(a__pairNs, pair(mark(z0), mark(z1)))) MARK(take(pairNs, x0)) -> c22(A__TAKE(cons(0, incr(oddNs)), mark(x0))) MARK(take(pairNs, x0)) -> c22(A__TAKE(pairNs, mark(x0))) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) 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A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> 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MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) 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c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(pairNs, 0)) -> c22(A__TAKE(a__pairNs, 0)) MARK(take(pairNs, s(z0))) -> c22(A__TAKE(a__pairNs, s(mark(z0)))) MARK(take(pairNs, nil)) -> c22(A__TAKE(a__pairNs, nil)) MARK(take(pairNs, pair(z0, z1))) -> c22(A__TAKE(a__pairNs, pair(mark(z0), mark(z1)))) MARK(take(pairNs, x0)) -> c22(A__TAKE(cons(0, incr(oddNs)), mark(x0))) MARK(take(pairNs, x0)) -> c22(A__TAKE(pairNs, mark(x0))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (221) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: MARK(take(pairNs, x0)) -> c22(A__TAKE(pairNs, mark(x0))) MARK(take(pairNs, x0)) -> c22(A__TAKE(cons(0, incr(oddNs)), mark(x0))) MARK(take(pairNs, nil)) -> c22(A__TAKE(a__pairNs, nil)) MARK(take(pairNs, 0)) -> c22(A__TAKE(a__pairNs, 0)) MARK(take(pairNs, pair(z0, z1))) -> c22(A__TAKE(a__pairNs, pair(mark(z0), mark(z1)))) MARK(take(pairNs, s(z0))) -> c22(A__TAKE(a__pairNs, s(mark(z0)))) ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), 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z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (223) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, incr(z0))) -> c23(A__TAKE(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) by MARK(take(x0, incr(x1))) -> c23(A__TAKE(mark(x0), incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0)), MARK(incr(0))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil)), MARK(incr(nil))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(cons(z0, z1), incr(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(A__TAKE(0, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(A__TAKE(nil, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) ---------------------------------------- (224) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> 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MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, repItems(z0)))) MARK(take(take(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(take(x0, cons(z0, z1)))) MARK(take(take(x0, 0), x2)) -> c22(A__TAKE(a__take(mark(x0), 0), mark(x2)), MARK(take(x0, 0))) MARK(take(take(x0, s(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), s(mark(z0))), mark(x2)), MARK(take(x0, s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(x0, incr(x1))) -> c23(A__TAKE(mark(x0), incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0)), MARK(incr(0))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil)), MARK(incr(nil))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(cons(z0, z1), incr(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(A__TAKE(0, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(A__TAKE(nil, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> 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c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(x0, incr(x1))) -> c23(A__TAKE(mark(x0), incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0)), MARK(incr(0))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil)), MARK(incr(nil))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(cons(z0, z1), incr(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(A__TAKE(0, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(A__TAKE(nil, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (225) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (226) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), 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a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> 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MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (227) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__oddNs), MARK(oddNs)) by MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), oddNs), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(oddNs)) MARK(take(0, oddNs)) -> c23(A__TAKE(0, a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(A__TAKE(nil, a__oddNs), MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) ---------------------------------------- (228) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), 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z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), 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-> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), oddNs), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(oddNs)) MARK(take(0, oddNs)) -> c23(A__TAKE(0, a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(A__TAKE(nil, a__oddNs), MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) 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MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) 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c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, 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s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), oddNs), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(A__TAKE(cons(mark(z0), z1), a__oddNs), MARK(oddNs)) MARK(take(0, oddNs)) -> c23(A__TAKE(0, a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(A__TAKE(nil, a__oddNs), MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (229) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (230) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> 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c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> 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c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), 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MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), 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c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, z1)), x1)) -> c22(A__TAKE(s(pair(mark(z0), mark(z1))), mark(x1)), MARK(s(pair(z0, z1)))) MARK(take(s(x0), x1)) -> c22(MARK(s(x0))) MARK(take(s(x0), 0)) -> c22(MARK(s(x0))) MARK(take(s(x0), s(z0))) -> c22(MARK(s(x0))) MARK(take(s(x0), nil)) -> c22(MARK(s(x0))) MARK(take(s(x0), pair(z0, z1))) -> c22(MARK(s(x0))) MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (231) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, take(z0, z1))) -> c23(A__TAKE(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) by MARK(take(x0, take(x1, x2))) -> c23(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) ---------------------------------------- (232) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), 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a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, x2))) -> c23(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> 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incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, x2))) -> c23(A__TAKE(mark(x0), take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(A__TAKE(0, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(A__TAKE(nil, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (233) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (234) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) 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MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), 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MARK(take(x0, incr(pairNs))) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(take(x0, incr(incr(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(take(x0, incr(oddNs))) -> c23(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(take(x0, incr(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(take(x0, incr(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(take(x0, incr(tail(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, 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c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), 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a__zip(mark(x1), cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, zip(x1, 0))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(x0)) MARK(take(x0, zip(x1, s(z0)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(x0)) MARK(take(x0, zip(x1, nil))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(x0)) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, zip(pairNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(incr(z0), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(x0)) MARK(take(x0, zip(oddNs, x2))) -> c22(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(x0)) MARK(take(x0, zip(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, zip(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(x0)) MARK(take(x0, 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a__zip(mark(x1), mark(x2))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(z0, z1))) MARK(take(tail(z0), zip(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(tail(z0))) MARK(take(repItems(z0), zip(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(repItems(z0))) MARK(take(s(z0), zip(x1, x2))) -> c22(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(s(z0))) MARK(take(x0, zip(x1, x2))) -> c22(MARK(x0)) MARK(take(pairNs, zip(x1, x2))) -> c22(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2)))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(pairNs))) -> c22(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(x0)) MARK(take(x0, tail(incr(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, tail(oddNs))) -> c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, repItems(incr(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(oddNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(x0)) MARK(take(x0, repItems(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, repItems(tail(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, repItems(0))) -> c22(A__TAKE(mark(x0), a__repItems(0)), MARK(x0)) MARK(take(x0, repItems(s(z0)))) -> c22(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(x0)) MARK(take(x0, repItems(nil))) -> c22(A__TAKE(mark(x0), a__repItems(nil)), MARK(x0)) MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, a__repItems(mark(x1)))) MARK(take(cons(z0, z1), repItems(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), repItems(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(pairNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(x0)) MARK(take(x0, cons(incr(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> 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a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (235) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, zip(z0, z1))) -> c23(A__TAKE(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) by MARK(take(x0, zip(x1, x2))) -> c23(A__TAKE(mark(x0), zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) ---------------------------------------- (236) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) 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x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> 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c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), 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c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) -> c22(A__TAKE(s(nil), mark(x1)), MARK(s(nil))) MARK(take(s(pair(z0, 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c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(A__TAKE(mark(x0), zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), 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x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), 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z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) 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z1), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(A__TAKE(0, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(A__TAKE(nil, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (237) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (238) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, 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zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), 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x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, 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c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__oddNs)), MARK(take(x1, oddNs))) MARK(take(x0, take(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__take(mark(z0), mark(z1)))), MARK(take(x1, take(z0, z1)))) MARK(take(x0, take(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(take(x1, zip(z0, z1)))) MARK(take(x0, take(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__tail(mark(z0)))), MARK(take(x1, tail(z0)))) MARK(take(x0, take(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__repItems(mark(z0)))), MARK(take(x1, repItems(z0)))) MARK(take(x0, take(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), cons(mark(z0), z1))), MARK(take(x1, cons(z0, z1)))) MARK(take(x0, take(x1, 0))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), 0)), MARK(take(x1, 0))) MARK(take(x0, take(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), s(mark(z0)))), MARK(take(x1, s(z0)))) MARK(take(x0, take(x1, nil))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (239) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, tail(z0))) -> c23(A__TAKE(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) by MARK(take(x0, tail(x1))) -> c23(A__TAKE(mark(x0), tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0)), MARK(tail(0))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil)), MARK(tail(nil))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(cons(z0, z1), tail(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(A__TAKE(0, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(A__TAKE(nil, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) ---------------------------------------- (240) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), 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MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(cons(z0, z1), tail(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(A__TAKE(0, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(A__TAKE(nil, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> 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c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) 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c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(x1))) -> c23(A__TAKE(mark(x0), tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0)), MARK(tail(0))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil)), MARK(tail(nil))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(cons(z0, z1), tail(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(A__TAKE(0, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(A__TAKE(nil, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (241) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (242) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), 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-> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> 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s(z0)))) MARK(take(take(x0, nil), x2)) -> c22(A__TAKE(a__take(mark(x0), nil), mark(x2)), MARK(take(x0, nil))) MARK(take(take(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, pair(z0, z1)))) MARK(take(take(pairNs, x1), x2)) -> c22(A__TAKE(a__take(a__pairNs, mark(x1)), mark(x2)), MARK(take(pairNs, x1))) MARK(take(take(incr(z0), x1), x2)) -> c22(A__TAKE(a__take(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(take(incr(z0), x1))) MARK(take(take(oddNs, x1), x2)) -> c22(A__TAKE(a__take(a__oddNs, mark(x1)), mark(x2)), MARK(take(oddNs, x1))) MARK(take(take(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, z1)))) MARK(take(zip(x0, tail(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(zip(x0, tail(z0)))) MARK(take(zip(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(zip(x0, repItems(z0)))) MARK(take(zip(x0, cons(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), cons(mark(z0), z1)), mark(x2)), MARK(zip(x0, cons(z0, z1)))) MARK(take(zip(x0, 0), x2)) -> c22(A__TAKE(a__zip(mark(x0), 0), mark(x2)), MARK(zip(x0, 0))) MARK(take(zip(x0, s(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), s(mark(z0))), mark(x2)), MARK(zip(x0, s(z0)))) MARK(take(zip(x0, nil), x2)) -> c22(A__TAKE(a__zip(mark(x0), nil), mark(x2)), MARK(zip(x0, nil))) MARK(take(zip(x0, pair(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), pair(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, pair(z0, z1)))) MARK(take(zip(pairNs, x1), x2)) -> c22(A__TAKE(a__zip(a__pairNs, mark(x1)), mark(x2)), MARK(zip(pairNs, x1))) MARK(take(zip(incr(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__incr(mark(z0)), mark(x1)), mark(x2)), MARK(zip(incr(z0), x1))) MARK(take(zip(oddNs, x1), x2)) -> c22(A__TAKE(a__zip(a__oddNs, mark(x1)), mark(x2)), MARK(zip(oddNs, x1))) MARK(take(zip(take(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(take(z0, z1), x1))) MARK(take(zip(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(zip(z0, z1), x1))) MARK(take(zip(tail(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(zip(tail(z0), x1))) MARK(take(zip(repItems(z0), x1), x2)) -> c22(A__TAKE(a__zip(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(zip(repItems(z0), x1))) MARK(take(zip(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(zip(cons(z0, z1), x1))) MARK(take(zip(0, x1), x2)) -> c22(A__TAKE(a__zip(0, mark(x1)), mark(x2)), MARK(zip(0, x1))) MARK(take(zip(s(z0), x1), x2)) -> c22(A__TAKE(a__zip(s(mark(z0)), mark(x1)), mark(x2)), MARK(zip(s(z0), x1))) MARK(take(zip(nil, x1), x2)) -> c22(A__TAKE(a__zip(nil, mark(x1)), mark(x2)), MARK(zip(nil, x1))) MARK(take(zip(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__zip(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(zip(pair(z0, z1), x1))) MARK(take(zip(x0, x1), 0)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), s(z0))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), nil)) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), pair(z0, z1))) -> c22(MARK(zip(x0, x1))) MARK(take(zip(x0, x1), x2)) -> c22(MARK(zip(x0, x1))) MARK(take(tail(pairNs), x1)) -> c22(A__TAKE(a__tail(a__pairNs), mark(x1)), MARK(tail(pairNs))) MARK(take(tail(incr(z0)), x1)) -> c22(A__TAKE(a__tail(a__incr(mark(z0))), mark(x1)), MARK(tail(incr(z0)))) MARK(take(tail(oddNs), x1)) -> c22(A__TAKE(a__tail(a__oddNs), mark(x1)), MARK(tail(oddNs))) MARK(take(tail(take(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__take(mark(z0), mark(z1))), mark(x1)), MARK(tail(take(z0, z1)))) MARK(take(tail(zip(z0, z1)), x1)) -> c22(A__TAKE(a__tail(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(tail(zip(z0, z1)))) MARK(take(tail(tail(z0)), x1)) -> c22(A__TAKE(a__tail(a__tail(mark(z0))), mark(x1)), MARK(tail(tail(z0)))) MARK(take(tail(repItems(z0)), x1)) -> c22(A__TAKE(a__tail(a__repItems(mark(z0))), mark(x1)), MARK(tail(repItems(z0)))) MARK(take(tail(cons(z0, z1)), x1)) -> c22(A__TAKE(a__tail(cons(mark(z0), z1)), mark(x1)), MARK(tail(cons(z0, z1)))) MARK(take(tail(s(z0)), x1)) -> c22(A__TAKE(a__tail(s(mark(z0))), mark(x1)), MARK(tail(s(z0)))) MARK(take(tail(pair(z0, z1)), x1)) -> c22(A__TAKE(a__tail(pair(mark(z0), mark(z1))), mark(x1)), MARK(tail(pair(z0, z1)))) MARK(take(tail(x0), 0)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), s(z0))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), nil)) -> c22(MARK(tail(x0))) MARK(take(tail(x0), pair(z0, z1))) -> c22(MARK(tail(x0))) MARK(take(tail(x0), x1)) -> c22(MARK(tail(x0))) MARK(take(tail(0), x1)) -> c22(A__TAKE(a__tail(0), mark(x1))) MARK(take(tail(nil), x1)) -> c22(A__TAKE(a__tail(nil), mark(x1))) MARK(take(repItems(pairNs), x1)) -> c22(A__TAKE(a__repItems(a__pairNs), mark(x1)), MARK(repItems(pairNs))) MARK(take(repItems(incr(z0)), x1)) -> c22(A__TAKE(a__repItems(a__incr(mark(z0))), mark(x1)), MARK(repItems(incr(z0)))) MARK(take(repItems(oddNs), x1)) -> c22(A__TAKE(a__repItems(a__oddNs), mark(x1)), MARK(repItems(oddNs))) MARK(take(repItems(take(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__take(mark(z0), mark(z1))), mark(x1)), MARK(repItems(take(z0, z1)))) MARK(take(repItems(zip(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(repItems(zip(z0, z1)))) MARK(take(repItems(tail(z0)), x1)) -> c22(A__TAKE(a__repItems(a__tail(mark(z0))), mark(x1)), MARK(repItems(tail(z0)))) MARK(take(repItems(repItems(z0)), x1)) -> c22(A__TAKE(a__repItems(a__repItems(mark(z0))), mark(x1)), MARK(repItems(repItems(z0)))) MARK(take(repItems(cons(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(cons(mark(z0), z1)), mark(x1)), MARK(repItems(cons(z0, z1)))) MARK(take(repItems(s(z0)), x1)) -> c22(A__TAKE(a__repItems(s(mark(z0))), mark(x1)), MARK(repItems(s(z0)))) MARK(take(repItems(pair(z0, z1)), x1)) -> c22(A__TAKE(a__repItems(pair(mark(z0), mark(z1))), mark(x1)), MARK(repItems(pair(z0, z1)))) MARK(take(repItems(x0), 0)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), s(z0))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), nil)) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), pair(z0, z1))) -> c22(MARK(repItems(x0))) MARK(take(repItems(x0), x1)) -> c22(MARK(repItems(x0))) MARK(take(repItems(0), x1)) -> c22(A__TAKE(a__repItems(0), mark(x1))) MARK(take(repItems(nil), x1)) -> c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), 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MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), 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mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (243) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, repItems(z0))) -> c23(A__TAKE(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) by MARK(take(x0, repItems(x1))) -> c23(A__TAKE(mark(x0), repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0)), MARK(repItems(0))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil)), MARK(repItems(nil))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(A__TAKE(0, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(A__TAKE(nil, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) ---------------------------------------- (244) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) 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c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(A__TAKE(0, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(A__TAKE(nil, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> 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MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) 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c22(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(x0)) MARK(take(x0, tail(take(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(zip(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(x0)) MARK(take(x0, tail(tail(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, 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MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, 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-> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, 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c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, 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z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(x1))) -> c23(A__TAKE(mark(x0), repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0)), MARK(repItems(0))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil)), MARK(repItems(nil))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(A__TAKE(cons(mark(z0), z1), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(A__TAKE(0, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(A__TAKE(nil, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (245) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (246) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) 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c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, 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a__tail(a__tail(mark(z0)))), MARK(x0)) MARK(take(x0, tail(repItems(z0)))) -> c22(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(x0)) MARK(take(x0, tail(cons(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(x0)) MARK(take(x0, tail(0))) -> c22(A__TAKE(mark(x0), a__tail(0)), MARK(x0)) MARK(take(x0, tail(s(z0)))) -> c22(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(x0)) MARK(take(x0, tail(nil))) -> c22(A__TAKE(mark(x0), a__tail(nil)), MARK(x0)) MARK(take(x0, tail(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), tail(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, 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MARK(x0)) MARK(take(x0, cons(oddNs, x2))) -> c22(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(x0)) MARK(take(x0, cons(take(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(zip(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(x0, cons(tail(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(repItems(z0), x2))) -> c22(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(cons(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(x0)) MARK(take(x0, cons(0, x2))) -> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) 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MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__repItems(mark(z0)), mark(x2))), MARK(take(repItems(z0), x2))) MARK(take(x0, take(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(cons(mark(z0), z1), mark(x2))), MARK(take(cons(z0, z1), x2))) MARK(take(x0, take(0, x2))) -> c23(A__TAKE(mark(x0), a__take(0, mark(x2))), MARK(take(0, x2))) MARK(take(x0, take(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(s(mark(z0)), mark(x2))), MARK(take(s(z0), x2))) MARK(take(x0, take(nil, x2))) -> c23(A__TAKE(mark(x0), a__take(nil, mark(x2))), MARK(take(nil, x2))) MARK(take(x0, take(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(pair(mark(z0), mark(z1)), mark(x2))), MARK(take(pair(z0, z1), x2))) MARK(take(pairNs, take(x1, x2))) -> c23(A__TAKE(a__pairNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(incr(z0), take(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(oddNs, take(x1, x2))) -> c23(A__TAKE(a__oddNs, a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (247) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(x0, cons(z0, z1))) -> c23(A__TAKE(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) by MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) ---------------------------------------- (248) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> 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c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), 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MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, 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MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> 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c22(A__TAKE(a__repItems(nil), mark(x1))) MARK(take(s(pairNs), x1)) -> c22(A__TAKE(s(a__pairNs), mark(x1)), MARK(s(pairNs))) MARK(take(s(incr(z0)), x1)) -> c22(A__TAKE(s(a__incr(mark(z0))), mark(x1)), MARK(s(incr(z0)))) MARK(take(s(oddNs), x1)) -> c22(A__TAKE(s(a__oddNs), mark(x1)), MARK(s(oddNs))) MARK(take(s(take(z0, z1)), x1)) -> c22(A__TAKE(s(a__take(mark(z0), mark(z1))), mark(x1)), MARK(s(take(z0, z1)))) MARK(take(s(zip(z0, z1)), x1)) -> c22(A__TAKE(s(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(s(zip(z0, z1)))) MARK(take(s(tail(z0)), x1)) -> c22(A__TAKE(s(a__tail(mark(z0))), mark(x1)), MARK(s(tail(z0)))) MARK(take(s(repItems(z0)), x1)) -> c22(A__TAKE(s(a__repItems(mark(z0))), mark(x1)), MARK(s(repItems(z0)))) MARK(take(s(cons(z0, z1)), x1)) -> c22(A__TAKE(s(cons(mark(z0), z1)), mark(x1)), MARK(s(cons(z0, z1)))) MARK(take(s(0), x1)) -> c22(A__TAKE(s(0), mark(x1)), MARK(s(0))) MARK(take(s(s(z0)), x1)) -> c22(A__TAKE(s(s(mark(z0))), mark(x1)), MARK(s(s(z0)))) MARK(take(s(nil), x1)) 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a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(take(x0, incr(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(take(x0, incr(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(take(x0, incr(s(z0)))) -> c23(A__TAKE(mark(x0), a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(take(x0, incr(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(take(pairNs, incr(x1))) -> c23(A__TAKE(a__pairNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(incr(z0), incr(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(oddNs, incr(x1))) -> c23(A__TAKE(a__oddNs, a__incr(mark(x1))), MARK(incr(x1))) MARK(take(take(z0, z1), incr(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(zip(z0, z1), incr(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(tail(z0), incr(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(repItems(z0), incr(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(s(z0), incr(x1))) -> c23(A__TAKE(s(mark(z0)), a__incr(mark(x1))), MARK(incr(x1))) MARK(take(x0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, incr(0))) -> c23(A__TAKE(mark(x0), a__incr(0))) MARK(take(x0, incr(nil))) -> c23(A__TAKE(mark(x0), a__incr(nil))) MARK(take(cons(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(0, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(nil, incr(x1))) -> c23(MARK(incr(x1))) MARK(take(pair(z0, z1), incr(x1))) -> c23(MARK(incr(x1))) MARK(take(x0, oddNs)) -> c23(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(oddNs)) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(incr(z0), oddNs)) -> c23(A__TAKE(a__incr(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(take(z0, z1), oddNs)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(zip(z0, z1), oddNs)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__oddNs), MARK(oddNs)) MARK(take(tail(z0), oddNs)) -> c23(A__TAKE(a__tail(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(repItems(z0), oddNs)) -> c23(A__TAKE(a__repItems(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(s(z0), oddNs)) -> c23(A__TAKE(s(mark(z0)), a__oddNs), MARK(oddNs)) MARK(take(x0, oddNs)) -> c23(MARK(oddNs)) MARK(take(cons(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(0, oddNs)) -> c23(MARK(oddNs)) MARK(take(nil, oddNs)) -> c23(MARK(oddNs)) MARK(take(pair(z0, z1), oddNs)) -> c23(MARK(oddNs)) MARK(take(x0, take(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__pairNs)), MARK(take(x1, pairNs))) MARK(take(x0, take(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), a__incr(mark(z0)))), MARK(take(x1, incr(z0)))) MARK(take(x0, take(x1, oddNs))) -> 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c23(A__TAKE(mark(x0), a__take(mark(x1), nil)), MARK(take(x1, nil))) MARK(take(x0, take(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__take(mark(x1), pair(mark(z0), mark(z1)))), MARK(take(x1, pair(z0, z1)))) MARK(take(x0, take(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__pairNs, mark(x2))), MARK(take(pairNs, x2))) MARK(take(x0, take(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__incr(mark(z0)), mark(x2))), MARK(take(incr(z0), x2))) MARK(take(x0, take(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__take(a__oddNs, mark(x2))), MARK(take(oddNs, x2))) MARK(take(x0, take(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__take(mark(z0), mark(z1)), mark(x2))), MARK(take(take(z0, z1), x2))) MARK(take(x0, take(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__take(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(take(zip(z0, z1), x2))) MARK(take(x0, take(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__take(a__tail(mark(z0)), mark(x2))), MARK(take(tail(z0), x2))) MARK(take(x0, take(repItems(z0), 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mark(x2))), MARK(take(x1, x2))) MARK(take(take(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> 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c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(A__TAKE(cons(mark(z0), z1), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(A__TAKE(0, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(A__TAKE(nil, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(A__TAKE(pair(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (249) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (250) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) 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MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), 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a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (251) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(pairNs, x1)) -> c23(A__TAKE(a__pairNs, mark(x1)), MARK(x1)) by MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(pairNs, incr(z0))) -> c23(A__TAKE(a__pairNs, a__incr(mark(z0))), MARK(incr(z0))) MARK(take(pairNs, oddNs)) -> c23(A__TAKE(a__pairNs, a__oddNs), MARK(oddNs)) MARK(take(pairNs, take(z0, z1))) -> c23(A__TAKE(a__pairNs, a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(pairNs, zip(z0, z1))) -> c23(A__TAKE(a__pairNs, a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(pairNs, tail(z0))) -> c23(A__TAKE(a__pairNs, a__tail(mark(z0))), MARK(tail(z0))) MARK(take(pairNs, repItems(z0))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(pairNs, cons(z0, z1))) -> c23(A__TAKE(a__pairNs, cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(pairNs, 0)) -> c23(A__TAKE(a__pairNs, 0), MARK(0)) MARK(take(pairNs, s(z0))) -> c23(A__TAKE(a__pairNs, s(mark(z0))), MARK(s(z0))) MARK(take(pairNs, nil)) -> c23(A__TAKE(a__pairNs, nil), MARK(nil)) MARK(take(pairNs, pair(z0, z1))) -> c23(A__TAKE(a__pairNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(A__TAKE(cons(0, incr(oddNs)), mark(x0)), MARK(x0)) MARK(take(pairNs, x0)) -> c23(A__TAKE(pairNs, mark(x0)), MARK(x0)) ---------------------------------------- (252) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, x1))) -> c20(A__INCR(a__zip(a__pairNs, mark(x1))), MARK(zip(pairNs, x1))) MARK(incr(zip(incr(z0), x1))) -> c20(A__INCR(a__zip(a__incr(mark(z0)), mark(x1))), MARK(zip(incr(z0), x1))) MARK(incr(zip(oddNs, x1))) -> c20(A__INCR(a__zip(a__oddNs, mark(x1))), MARK(zip(oddNs, x1))) MARK(incr(zip(take(z0, z1), x1))) -> c20(A__INCR(a__zip(a__take(mark(z0), mark(z1)), mark(x1))), MARK(zip(take(z0, z1), x1))) MARK(incr(zip(zip(z0, z1), x1))) -> c20(A__INCR(a__zip(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(zip(zip(z0, z1), x1))) MARK(incr(zip(tail(z0), x1))) -> c20(A__INCR(a__zip(a__tail(mark(z0)), mark(x1))), MARK(zip(tail(z0), x1))) MARK(incr(zip(repItems(z0), x1))) -> c20(A__INCR(a__zip(a__repItems(mark(z0)), mark(x1))), MARK(zip(repItems(z0), x1))) MARK(incr(zip(cons(z0, z1), x1))) -> c20(A__INCR(a__zip(cons(mark(z0), z1), mark(x1))), MARK(zip(cons(z0, z1), x1))) MARK(incr(zip(0, x1))) -> c20(A__INCR(a__zip(0, mark(x1))), MARK(zip(0, x1))) MARK(incr(zip(s(z0), x1))) -> c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(incr(tail(cons(z0, z1)))) -> c20(A__INCR(a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(incr(tail(s(z0)))) -> c20(A__INCR(a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(incr(tail(pair(z0, z1)))) -> c20(A__INCR(a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) 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MARK(incr(z0))) MARK(take(oddNs, tail(x1))) -> c22(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), tail(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), tail(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), tail(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), tail(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), tail(x1))) -> c22(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(s(z0))) MARK(take(x0, tail(x1))) -> c22(MARK(x0)) MARK(take(pairNs, tail(x1))) -> c22(A__TAKE(a__pairNs, a__tail(mark(x1)))) MARK(take(cons(z0, z1), tail(x1))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), tail(x1))) -> c22(MARK(pair(z0, z1))) MARK(take(x0, repItems(pairNs))) -> c22(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(x0)) MARK(take(x0, 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MARK(take(x0, repItems(pair(z0, z1)))) -> c22(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(x0)) MARK(take(incr(z0), repItems(x1))) -> c22(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(incr(z0))) MARK(take(oddNs, repItems(x1))) -> c22(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(oddNs)) MARK(take(take(z0, z1), repItems(x1))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(take(z0, z1))) MARK(take(zip(z0, z1), repItems(x1))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(zip(z0, z1))) MARK(take(tail(z0), repItems(x1))) -> c22(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(tail(z0))) MARK(take(repItems(z0), repItems(x1))) -> c22(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(z0))) MARK(take(s(z0), repItems(x1))) -> c22(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(s(z0))) MARK(take(x0, repItems(x1))) -> c22(MARK(x0)) MARK(take(pairNs, repItems(x1))) -> c22(A__TAKE(a__pairNs, 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-> c22(A__TAKE(mark(x0), cons(0, x2)), MARK(x0)) MARK(take(x0, cons(s(z0), x2))) -> c22(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(x0)) MARK(take(x0, cons(nil, x2))) -> c22(A__TAKE(mark(x0), cons(nil, x2)), MARK(x0)) MARK(take(x0, cons(pair(z0, z1), x2))) -> c22(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(x0)) MARK(take(incr(z0), cons(x1, x2))) -> c22(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(incr(z0))) MARK(take(oddNs, cons(x1, x2))) -> c22(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(oddNs)) MARK(take(take(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(take(z0, z1))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(zip(z0, z1))) MARK(take(tail(z0), cons(x1, x2))) -> c22(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(tail(z0))) MARK(take(repItems(z0), cons(x1, x2))) -> c22(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(repItems(z0))) MARK(take(s(z0), cons(x1, x2))) -> c22(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(s(z0))) MARK(take(pairNs, cons(x1, x2))) -> c22(A__TAKE(a__pairNs, cons(mark(x1), x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c22(MARK(pair(z0, z1))) MARK(take(incr(pairNs), x1)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(incr(pairNs))) MARK(take(incr(incr(z0)), x1)) -> c22(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(incr(incr(z0)))) MARK(take(incr(oddNs), x1)) -> c22(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(incr(oddNs))) MARK(take(incr(take(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(incr(take(z0, z1)))) MARK(take(incr(zip(z0, z1)), x1)) -> c22(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(incr(zip(z0, z1)))) MARK(take(incr(tail(z0)), x1)) -> c22(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(incr(tail(z0)))) MARK(take(incr(repItems(z0)), x1)) -> c22(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(incr(repItems(z0)))) MARK(take(incr(cons(z0, z1)), x1)) -> c22(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(incr(cons(z0, z1)))) MARK(take(incr(s(z0)), x1)) -> c22(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(incr(s(z0)))) MARK(take(incr(pair(z0, z1)), x1)) -> c22(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(incr(pair(z0, z1)))) MARK(take(incr(x0), 0)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), s(z0))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), nil)) -> c22(MARK(incr(x0))) MARK(take(incr(x0), pair(z0, z1))) -> c22(MARK(incr(x0))) MARK(take(incr(x0), x1)) -> c22(MARK(incr(x0))) MARK(take(incr(0), x1)) -> c22(A__TAKE(a__incr(0), mark(x1))) MARK(take(incr(nil), x1)) -> c22(A__TAKE(a__incr(nil), mark(x1))) MARK(take(oddNs, x0)) -> c22(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(oddNs)) MARK(take(oddNs, 0)) -> c22(MARK(oddNs)) MARK(take(oddNs, s(z0))) -> c22(MARK(oddNs)) MARK(take(oddNs, nil)) -> c22(MARK(oddNs)) MARK(take(oddNs, pair(z0, z1))) -> c22(MARK(oddNs)) MARK(take(oddNs, x0)) -> c22(MARK(oddNs)) MARK(take(take(x0, pairNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__pairNs), mark(x2)), MARK(take(x0, pairNs))) MARK(take(take(x0, incr(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(take(x0, incr(z0)))) MARK(take(take(x0, oddNs), x2)) -> c22(A__TAKE(a__take(mark(x0), a__oddNs), mark(x2)), MARK(take(x0, oddNs))) MARK(take(take(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, take(z0, z1)))) MARK(take(take(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(take(x0, zip(z0, z1)))) MARK(take(take(x0, tail(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__tail(mark(z0))), mark(x2)), MARK(take(x0, tail(z0)))) MARK(take(take(x0, repItems(z0)), x2)) -> c22(A__TAKE(a__take(mark(x0), a__repItems(mark(z0))), mark(x2)), MARK(take(x0, 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c22(A__TAKE(a__take(a__take(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(take(z0, z1), x1))) MARK(take(take(zip(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(a__zip(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(zip(z0, z1), x1))) MARK(take(take(tail(z0), x1), x2)) -> c22(A__TAKE(a__take(a__tail(mark(z0)), mark(x1)), mark(x2)), MARK(take(tail(z0), x1))) MARK(take(take(repItems(z0), x1), x2)) -> c22(A__TAKE(a__take(a__repItems(mark(z0)), mark(x1)), mark(x2)), MARK(take(repItems(z0), x1))) MARK(take(take(cons(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(cons(mark(z0), z1), mark(x1)), mark(x2)), MARK(take(cons(z0, z1), x1))) MARK(take(take(0, x1), x2)) -> c22(A__TAKE(a__take(0, mark(x1)), mark(x2)), MARK(take(0, x1))) MARK(take(take(s(z0), x1), x2)) -> c22(A__TAKE(a__take(s(mark(z0)), mark(x1)), mark(x2)), MARK(take(s(z0), x1))) MARK(take(take(nil, x1), x2)) -> c22(A__TAKE(a__take(nil, mark(x1)), mark(x2)), MARK(take(nil, x1))) MARK(take(take(pair(z0, z1), x1), x2)) -> c22(A__TAKE(a__take(pair(mark(z0), mark(z1)), mark(x1)), mark(x2)), MARK(take(pair(z0, z1), x1))) MARK(take(take(x0, x1), 0)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), s(z0))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), nil)) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), pair(z0, z1))) -> c22(MARK(take(x0, x1))) MARK(take(take(x0, x1), x2)) -> c22(MARK(take(x0, x1))) MARK(take(zip(x0, pairNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__pairNs), mark(x2)), MARK(zip(x0, pairNs))) MARK(take(zip(x0, incr(z0)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__incr(mark(z0))), mark(x2)), MARK(zip(x0, incr(z0)))) MARK(take(zip(x0, oddNs), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__oddNs), mark(x2)), MARK(zip(x0, oddNs))) MARK(take(zip(x0, take(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__take(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, take(z0, z1)))) MARK(take(zip(x0, zip(z0, z1)), x2)) -> c22(A__TAKE(a__zip(mark(x0), a__zip(mark(z0), mark(z1))), mark(x2)), MARK(zip(x0, zip(z0, 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MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, 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c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), 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MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> 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-> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(pairNs, 0)) -> c23(A__TAKE(a__pairNs, 0), MARK(0)) MARK(take(pairNs, s(z0))) -> c23(A__TAKE(a__pairNs, s(mark(z0))), MARK(s(z0))) MARK(take(pairNs, nil)) -> c23(A__TAKE(a__pairNs, nil), MARK(nil)) MARK(take(pairNs, pair(z0, z1))) -> c23(A__TAKE(a__pairNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(A__TAKE(cons(0, incr(oddNs)), mark(x0)), MARK(x0)) MARK(take(pairNs, x0)) -> c23(A__TAKE(pairNs, mark(x0)), MARK(x0)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> 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c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), 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a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(pairNs, 0)) -> c23(A__TAKE(a__pairNs, 0), MARK(0)) MARK(take(pairNs, s(z0))) -> c23(A__TAKE(a__pairNs, s(mark(z0))), MARK(s(z0))) MARK(take(pairNs, nil)) -> c23(A__TAKE(a__pairNs, nil), MARK(nil)) MARK(take(pairNs, pair(z0, z1))) -> c23(A__TAKE(a__pairNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(A__TAKE(cons(0, incr(oddNs)), mark(x0)), MARK(x0)) MARK(take(pairNs, x0)) -> c23(A__TAKE(pairNs, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (253) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(pairNs, 0)) -> c23(A__TAKE(a__pairNs, 0), MARK(0)) MARK(take(pairNs, nil)) -> c23(A__TAKE(a__pairNs, nil), MARK(nil)) ---------------------------------------- (254) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), 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MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(pairNs, s(z0))) -> c23(A__TAKE(a__pairNs, s(mark(z0))), MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(A__TAKE(a__pairNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(A__TAKE(cons(0, incr(oddNs)), mark(x0)), MARK(x0)) MARK(take(pairNs, x0)) -> c23(A__TAKE(pairNs, mark(x0)), MARK(x0)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), 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MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> 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-> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(zip(z0, z1), take(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(tail(z0), take(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(repItems(z0), take(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(s(z0), take(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__take(mark(x1), mark(x2))), MARK(take(x1, x2))) MARK(take(x0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(cons(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(0, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(nil, take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(pair(z0, z1), take(x1, x2))) -> c23(MARK(take(x1, x2))) MARK(take(x0, zip(x1, pairNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__pairNs)), MARK(zip(x1, pairNs))) MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs), MARK(pairNs)) MARK(take(pairNs, s(z0))) -> c23(A__TAKE(a__pairNs, s(mark(z0))), MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(A__TAKE(a__pairNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(A__TAKE(cons(0, incr(oddNs)), mark(x0)), MARK(x0)) MARK(take(pairNs, x0)) -> c23(A__TAKE(pairNs, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (255) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (256) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), 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tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs)) MARK(take(pairNs, s(z0))) -> c23(MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(MARK(x0)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (257) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(incr(z0), x1)) -> c23(A__TAKE(a__incr(mark(z0)), mark(x1)), MARK(x1)) by MARK(take(incr(x0), pairNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__pairNs), MARK(pairNs)) MARK(take(incr(x0), incr(z0))) -> c23(A__TAKE(a__incr(mark(x0)), a__incr(mark(z0))), MARK(incr(z0))) MARK(take(incr(x0), oddNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__oddNs), MARK(oddNs)) MARK(take(incr(x0), take(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(incr(x0), zip(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(incr(x0), tail(z0))) -> c23(A__TAKE(a__incr(mark(x0)), a__tail(mark(z0))), MARK(tail(z0))) MARK(take(incr(x0), repItems(z0))) -> c23(A__TAKE(a__incr(mark(x0)), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(incr(x0), cons(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(incr(x0), 0)) -> c23(A__TAKE(a__incr(mark(x0)), 0), MARK(0)) MARK(take(incr(x0), s(z0))) -> c23(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(incr(x0), nil)) -> c23(A__TAKE(a__incr(mark(x0)), nil), MARK(nil)) MARK(take(incr(x0), pair(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(incr(x0), x1)) -> c23(A__TAKE(incr(mark(x0)), mark(x1)), MARK(x1)) MARK(take(incr(pairNs), x1)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(x1)) MARK(take(incr(incr(z0)), x1)) -> c23(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(oddNs), x1)) -> c23(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(x1)) MARK(take(incr(take(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(zip(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(tail(z0)), x1)) -> c23(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(repItems(z0)), x1)) -> c23(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(cons(z0, z1)), x1)) -> c23(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(incr(0), x1)) -> c23(A__TAKE(a__incr(0), mark(x1)), MARK(x1)) MARK(take(incr(s(z0)), x1)) -> c23(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(nil), x1)) -> c23(A__TAKE(a__incr(nil), mark(x1)), MARK(x1)) MARK(take(incr(pair(z0, z1)), x1)) -> c23(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(x1)) ---------------------------------------- (258) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> 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mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs)) MARK(take(pairNs, s(z0))) -> c23(MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(MARK(x0)) MARK(take(incr(x0), pairNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__pairNs), MARK(pairNs)) MARK(take(incr(x0), 0)) -> c23(A__TAKE(a__incr(mark(x0)), 0), MARK(0)) MARK(take(incr(x0), s(z0))) -> c23(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(incr(x0), nil)) -> c23(A__TAKE(a__incr(mark(x0)), nil), MARK(nil)) MARK(take(incr(x0), pair(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(incr(x0), x1)) -> c23(A__TAKE(incr(mark(x0)), mark(x1)), MARK(x1)) MARK(take(incr(pairNs), x1)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(x1)) MARK(take(incr(incr(z0)), x1)) -> c23(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(oddNs), x1)) -> c23(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(x1)) MARK(take(incr(take(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(zip(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(tail(z0)), x1)) -> c23(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(repItems(z0)), x1)) -> c23(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(cons(z0, z1)), x1)) -> c23(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(incr(0), x1)) -> c23(A__TAKE(a__incr(0), mark(x1)), MARK(x1)) MARK(take(incr(s(z0)), x1)) -> c23(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(nil), x1)) -> c23(A__TAKE(a__incr(nil), mark(x1)), MARK(x1)) MARK(take(incr(pair(z0, z1)), x1)) -> c23(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> 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MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs)) MARK(take(pairNs, s(z0))) -> c23(MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(MARK(x0)) MARK(take(incr(x0), pairNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__pairNs), MARK(pairNs)) MARK(take(incr(x0), 0)) -> c23(A__TAKE(a__incr(mark(x0)), 0), MARK(0)) MARK(take(incr(x0), s(z0))) -> c23(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(incr(x0), nil)) -> c23(A__TAKE(a__incr(mark(x0)), nil), MARK(nil)) MARK(take(incr(x0), pair(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(incr(x0), x1)) -> c23(A__TAKE(incr(mark(x0)), mark(x1)), MARK(x1)) MARK(take(incr(pairNs), x1)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(x1)) MARK(take(incr(incr(z0)), x1)) -> c23(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(oddNs), x1)) -> c23(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(x1)) MARK(take(incr(take(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(zip(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(tail(z0)), x1)) -> c23(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(repItems(z0)), x1)) -> c23(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(cons(z0, z1)), x1)) -> c23(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(incr(0), x1)) -> c23(A__TAKE(a__incr(0), mark(x1)), MARK(x1)) MARK(take(incr(s(z0)), x1)) -> c23(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(nil), x1)) -> c23(A__TAKE(a__incr(nil), mark(x1)), MARK(x1)) MARK(take(incr(pair(z0, z1)), x1)) -> c23(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (259) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(incr(x0), 0)) -> c23(A__TAKE(a__incr(mark(x0)), 0), MARK(0)) MARK(take(incr(x0), nil)) -> c23(A__TAKE(a__incr(mark(x0)), nil), MARK(nil)) ---------------------------------------- (260) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), 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MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, repItems(z0)))) MARK(incr(zip(x0, cons(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), cons(mark(z0), z1))), MARK(zip(x0, cons(z0, z1)))) MARK(incr(zip(x0, 0))) -> c20(A__INCR(a__zip(mark(x0), 0)), MARK(zip(x0, 0))) MARK(incr(zip(x0, s(z0)))) -> c20(A__INCR(a__zip(mark(x0), s(mark(z0)))), MARK(zip(x0, s(z0)))) MARK(incr(zip(x0, nil))) -> c20(A__INCR(a__zip(mark(x0), nil)), MARK(zip(x0, nil))) MARK(incr(zip(x0, pair(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), pair(mark(z0), mark(z1)))), MARK(zip(x0, pair(z0, z1)))) MARK(incr(zip(pairNs, 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c20(A__INCR(a__zip(s(mark(z0)), mark(x1))), MARK(zip(s(z0), x1))) MARK(incr(zip(nil, x1))) -> c20(A__INCR(a__zip(nil, mark(x1))), MARK(zip(nil, x1))) MARK(incr(zip(pair(z0, z1), x1))) -> c20(A__INCR(a__zip(pair(mark(z0), mark(z1)), mark(x1))), MARK(zip(pair(z0, z1), x1))) MARK(incr(zip(x0, x1))) -> c20(MARK(zip(x0, x1))) MARK(incr(tail(pairNs))) -> c20(A__INCR(a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(incr(tail(incr(z0)))) -> c20(A__INCR(a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(incr(tail(oddNs))) -> c20(A__INCR(a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(incr(tail(take(z0, z1)))) -> c20(A__INCR(a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(incr(tail(zip(z0, z1)))) -> c20(A__INCR(a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(incr(tail(tail(z0)))) -> c20(A__INCR(a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(incr(tail(repItems(z0)))) -> c20(A__INCR(a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) 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c20(A__INCR(a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(incr(repItems(repItems(z0)))) -> c20(A__INCR(a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(incr(repItems(cons(z0, z1)))) -> c20(A__INCR(a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(incr(repItems(s(z0)))) -> c20(A__INCR(a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(incr(repItems(pair(z0, z1)))) -> c20(A__INCR(a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(incr(repItems(x0))) -> c20(MARK(repItems(x0))) MARK(incr(repItems(0))) -> c20(A__INCR(a__repItems(0))) MARK(incr(repItems(nil))) -> c20(A__INCR(a__repItems(nil))) MARK(incr(pairNs)) -> c20(A__INCR(cons(0, incr(oddNs)))) MARK(take(x0, pairNs)) -> c22(A__TAKE(mark(x0), cons(0, incr(oddNs))), MARK(x0)) MARK(take(incr(z0), pairNs)) -> c22(A__TAKE(a__incr(mark(z0)), a__pairNs), MARK(incr(z0))) MARK(take(oddNs, pairNs)) -> c22(A__TAKE(a__oddNs, a__pairNs), MARK(oddNs)) MARK(take(take(z0, z1), pairNs)) -> c22(A__TAKE(a__take(mark(z0), mark(z1)), a__pairNs), MARK(take(z0, z1))) MARK(take(zip(z0, z1), pairNs)) -> c22(A__TAKE(a__zip(mark(z0), mark(z1)), a__pairNs), MARK(zip(z0, z1))) MARK(take(tail(z0), pairNs)) -> c22(A__TAKE(a__tail(mark(z0)), a__pairNs), MARK(tail(z0))) MARK(take(repItems(z0), pairNs)) -> c22(A__TAKE(a__repItems(mark(z0)), a__pairNs), MARK(repItems(z0))) MARK(take(s(z0), pairNs)) -> c22(A__TAKE(s(mark(z0)), a__pairNs), MARK(s(z0))) MARK(take(x0, pairNs)) -> c22(MARK(x0)) MARK(take(pairNs, pairNs)) -> c22(A__TAKE(a__pairNs, a__pairNs)) MARK(take(cons(z0, z1), pairNs)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), pairNs)) -> c22(MARK(pair(z0, z1))) MARK(take(x0, incr(pairNs))) -> c22(A__TAKE(mark(x0), a__incr(a__pairNs)), MARK(x0)) MARK(take(x0, incr(incr(z0)))) -> c22(A__TAKE(mark(x0), a__incr(a__incr(mark(z0)))), MARK(x0)) MARK(take(x0, incr(oddNs))) -> c22(A__TAKE(mark(x0), a__incr(a__oddNs)), MARK(x0)) MARK(take(x0, 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-> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) 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MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), 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c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) 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MARK(take(x0, zip(x1, incr(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__incr(mark(z0)))), MARK(zip(x1, incr(z0)))) MARK(take(x0, zip(x1, oddNs))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__oddNs)), MARK(zip(x1, oddNs))) MARK(take(x0, zip(x1, take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__take(mark(z0), mark(z1)))), MARK(zip(x1, take(z0, z1)))) MARK(take(x0, zip(x1, zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__zip(mark(z0), mark(z1)))), MARK(zip(x1, zip(z0, z1)))) MARK(take(x0, zip(x1, tail(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__tail(mark(z0)))), MARK(zip(x1, tail(z0)))) MARK(take(x0, zip(x1, repItems(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), a__repItems(mark(z0)))), MARK(zip(x1, repItems(z0)))) MARK(take(x0, zip(x1, cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), cons(mark(z0), z1))), MARK(zip(x1, cons(z0, z1)))) MARK(take(x0, zip(x1, 0))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), 0)), MARK(zip(x1, 0))) MARK(take(x0, zip(x1, s(z0)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), s(mark(z0)))), MARK(zip(x1, s(z0)))) MARK(take(x0, zip(x1, nil))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), nil)), MARK(zip(x1, nil))) MARK(take(x0, zip(x1, pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__zip(mark(x1), pair(mark(z0), mark(z1)))), MARK(zip(x1, pair(z0, z1)))) MARK(take(x0, zip(pairNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__pairNs, mark(x2))), MARK(zip(pairNs, x2))) MARK(take(x0, zip(incr(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__incr(mark(z0)), mark(x2))), MARK(zip(incr(z0), x2))) MARK(take(x0, zip(oddNs, x2))) -> c23(A__TAKE(mark(x0), a__zip(a__oddNs, mark(x2))), MARK(zip(oddNs, x2))) MARK(take(x0, zip(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__take(mark(z0), mark(z1)), mark(x2))), MARK(zip(take(z0, z1), x2))) MARK(take(x0, zip(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__zip(mark(z0), mark(z1)), mark(x2))), MARK(zip(zip(z0, z1), x2))) MARK(take(x0, zip(tail(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__tail(mark(z0)), mark(x2))), MARK(zip(tail(z0), x2))) MARK(take(x0, zip(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(a__repItems(mark(z0)), mark(x2))), MARK(zip(repItems(z0), x2))) MARK(take(x0, zip(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(cons(mark(z0), z1), mark(x2))), MARK(zip(cons(z0, z1), x2))) MARK(take(x0, zip(0, x2))) -> c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs)) MARK(take(pairNs, s(z0))) -> c23(MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(MARK(x0)) MARK(take(incr(x0), pairNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__pairNs), MARK(pairNs)) MARK(take(incr(x0), s(z0))) -> c23(A__TAKE(a__incr(mark(x0)), s(mark(z0))), MARK(s(z0))) MARK(take(incr(x0), pair(z0, z1))) -> c23(A__TAKE(a__incr(mark(x0)), pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(incr(x0), x1)) -> c23(A__TAKE(incr(mark(x0)), mark(x1)), MARK(x1)) MARK(take(incr(pairNs), x1)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(x1)) MARK(take(incr(incr(z0)), x1)) -> c23(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(oddNs), x1)) -> c23(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(x1)) MARK(take(incr(take(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(zip(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(tail(z0)), x1)) -> c23(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(repItems(z0)), x1)) -> c23(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(cons(z0, z1)), x1)) -> c23(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(incr(0), x1)) -> c23(A__TAKE(a__incr(0), mark(x1)), MARK(x1)) MARK(take(incr(s(z0)), x1)) -> c23(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(nil), x1)) -> c23(A__TAKE(a__incr(nil), mark(x1)), MARK(x1)) MARK(take(incr(pair(z0, z1)), x1)) -> c23(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2 ---------------------------------------- (261) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (262) Obligation: Complexity Dependency Tuples Problem Rules: a__pairNs -> cons(0, incr(oddNs)) a__pairNs -> pairNs a__oddNs -> a__incr(a__pairNs) a__oddNs -> oddNs a__incr(cons(z0, z1)) -> cons(s(mark(z0)), incr(z1)) a__incr(z0) -> incr(z0) a__take(0, z0) -> nil a__take(s(z0), cons(z1, z2)) -> cons(mark(z1), take(z0, z2)) a__take(z0, z1) -> take(z0, z1) a__zip(nil, z0) -> nil a__zip(z0, nil) -> nil a__zip(cons(z0, z1), cons(z2, z3)) -> cons(pair(mark(z0), mark(z2)), zip(z1, z3)) a__zip(z0, z1) -> zip(z0, z1) a__tail(cons(z0, z1)) -> mark(z1) a__tail(z0) -> tail(z0) a__repItems(nil) -> nil a__repItems(cons(z0, z1)) -> cons(mark(z0), cons(z0, repItems(z1))) a__repItems(z0) -> repItems(z0) mark(pairNs) -> a__pairNs mark(incr(z0)) -> a__incr(mark(z0)) mark(oddNs) -> a__oddNs mark(take(z0, z1)) -> a__take(mark(z0), mark(z1)) mark(zip(z0, z1)) -> a__zip(mark(z0), mark(z1)) mark(tail(z0)) -> a__tail(mark(z0)) mark(repItems(z0)) -> a__repItems(mark(z0)) mark(cons(z0, z1)) -> cons(mark(z0), z1) mark(0) -> 0 mark(s(z0)) -> s(mark(z0)) mark(nil) -> nil mark(pair(z0, z1)) -> pair(mark(z0), mark(z1)) Tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> c28(MARK(z0)) MARK(s(z0)) -> c30(MARK(z0)) MARK(pair(z0, z1)) -> c32(MARK(z0)) MARK(pair(z0, z1)) -> c33(MARK(z1)) MARK(incr(cons(z0, z1))) -> c20(A__INCR(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(incr(s(z0))) -> c20(MARK(s(z0))) MARK(incr(pair(z0, z1))) -> c20(MARK(pair(z0, z1))) MARK(take(x0, 0)) -> c22(MARK(x0)) MARK(take(x0, s(z0))) -> c22(MARK(x0)) MARK(take(x0, nil)) -> c22(MARK(x0)) MARK(take(x0, pair(z0, z1))) -> c22(MARK(x0)) MARK(take(cons(z0, z1), x1)) -> c22(MARK(cons(z0, z1))) MARK(take(pair(z0, z1), x1)) -> c22(MARK(pair(z0, z1))) MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) MARK(take(take(z0, z1), x1)) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(zip(z0, z1), x1)) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(take(tail(z0), x1)) -> c23(A__TAKE(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(take(repItems(z0), x1)) -> c23(A__TAKE(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(take(s(z0), x1)) -> c23(A__TAKE(s(mark(z0)), mark(x1)), MARK(x1)) MARK(take(x0, pairNs)) -> c23(A__TAKE(mark(x0), a__pairNs)) MARK(take(x0, s(z0))) -> c23(MARK(s(z0))) MARK(take(x0, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(cons(z0, z1), x1)) -> c23(MARK(x1)) MARK(take(0, x1)) -> c23(MARK(x1)) MARK(take(nil, x1)) -> c23(MARK(x1)) MARK(take(pair(z0, z1), x1)) -> c23(MARK(x1)) MARK(zip(x0, pairNs)) -> c24(A__ZIP(mark(x0), a__pairNs), MARK(x0)) MARK(zip(x0, incr(z0))) -> c24(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(x0)) MARK(zip(x0, oddNs)) -> c24(A__ZIP(mark(x0), a__oddNs), MARK(x0)) MARK(zip(x0, take(z0, z1))) -> c24(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, zip(z0, z1))) -> c24(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(x0)) MARK(zip(x0, tail(z0))) -> c24(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(x0)) MARK(zip(x0, repItems(z0))) -> c24(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(x0)) MARK(zip(x0, cons(z0, z1))) -> c24(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(x0)) MARK(zip(incr(z0), x1)) -> c24(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(incr(z0))) MARK(zip(oddNs, x1)) -> c24(A__ZIP(a__oddNs, mark(x1)), MARK(oddNs)) MARK(zip(take(z0, z1), x1)) -> c24(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(take(z0, z1))) MARK(zip(zip(z0, z1), x1)) -> c24(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(zip(z0, z1))) MARK(zip(tail(z0), x1)) -> c24(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(tail(z0))) MARK(zip(repItems(z0), x1)) -> c24(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(repItems(z0))) MARK(zip(cons(z0, z1), x1)) -> c24(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(cons(z0, z1))) MARK(zip(x0, 0)) -> c24(MARK(x0)) MARK(zip(x0, s(z0))) -> c24(MARK(x0)) MARK(zip(x0, nil)) -> c24(MARK(x0)) MARK(zip(x0, pair(z0, z1))) -> c24(MARK(x0)) MARK(zip(pairNs, x1)) -> c24(A__ZIP(a__pairNs, mark(x1))) MARK(zip(s(z0), x1)) -> c24(MARK(s(z0))) MARK(zip(pair(z0, z1), x1)) -> c24(MARK(pair(z0, z1))) MARK(zip(x0, incr(z0))) -> c25(A__ZIP(mark(x0), a__incr(mark(z0))), MARK(incr(z0))) MARK(zip(x0, oddNs)) -> c25(A__ZIP(mark(x0), a__oddNs), MARK(oddNs)) MARK(zip(x0, take(z0, z1))) -> c25(A__ZIP(mark(x0), a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(zip(x0, zip(z0, z1))) -> c25(A__ZIP(mark(x0), a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(zip(x0, tail(z0))) -> c25(A__ZIP(mark(x0), a__tail(mark(z0))), MARK(tail(z0))) MARK(zip(x0, repItems(z0))) -> c25(A__ZIP(mark(x0), a__repItems(mark(z0))), MARK(repItems(z0))) MARK(zip(x0, cons(z0, z1))) -> c25(A__ZIP(mark(x0), cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(zip(pairNs, x1)) -> c25(A__ZIP(a__pairNs, mark(x1)), MARK(x1)) MARK(zip(incr(z0), x1)) -> c25(A__ZIP(a__incr(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(oddNs, x1)) -> c25(A__ZIP(a__oddNs, mark(x1)), MARK(x1)) MARK(zip(take(z0, z1), x1)) -> c25(A__ZIP(a__take(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(zip(z0, z1), x1)) -> c25(A__ZIP(a__zip(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(zip(tail(z0), x1)) -> c25(A__ZIP(a__tail(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(repItems(z0), x1)) -> c25(A__ZIP(a__repItems(mark(z0)), mark(x1)), MARK(x1)) MARK(zip(cons(z0, z1), x1)) -> c25(A__ZIP(cons(mark(z0), z1), mark(x1)), MARK(x1)) MARK(zip(x0, pairNs)) -> c25(A__ZIP(mark(x0), a__pairNs)) MARK(zip(x0, s(z0))) -> c25(MARK(s(z0))) MARK(zip(x0, pair(z0, z1))) -> c25(MARK(pair(z0, z1))) MARK(zip(0, x1)) -> c25(MARK(x1)) MARK(zip(s(z0), x1)) -> c25(MARK(x1)) MARK(zip(nil, x1)) -> c25(MARK(x1)) MARK(zip(pair(z0, z1), x1)) -> c25(MARK(x1)) MARK(tail(incr(z0))) -> c26(A__TAIL(a__incr(mark(z0))), MARK(incr(z0))) MARK(tail(oddNs)) -> c26(A__TAIL(a__oddNs), MARK(oddNs)) MARK(tail(take(z0, z1))) -> c26(A__TAIL(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(tail(zip(z0, z1))) -> c26(A__TAIL(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(tail(tail(z0))) -> c26(A__TAIL(a__tail(mark(z0))), MARK(tail(z0))) MARK(tail(repItems(z0))) -> c26(A__TAIL(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(tail(cons(z0, z1))) -> c26(A__TAIL(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(tail(pairNs)) -> c26(A__TAIL(a__pairNs)) MARK(tail(s(z0))) -> c26(MARK(s(z0))) MARK(tail(pair(z0, z1))) -> c26(MARK(pair(z0, z1))) MARK(repItems(incr(z0))) -> c27(A__REPITEMS(a__incr(mark(z0))), MARK(incr(z0))) MARK(repItems(oddNs)) -> c27(A__REPITEMS(a__oddNs), MARK(oddNs)) MARK(repItems(take(z0, z1))) -> c27(A__REPITEMS(a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(repItems(zip(z0, z1))) -> c27(A__REPITEMS(a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(repItems(tail(z0))) -> c27(A__REPITEMS(a__tail(mark(z0))), MARK(tail(z0))) MARK(repItems(repItems(z0))) -> c27(A__REPITEMS(a__repItems(mark(z0))), MARK(repItems(z0))) MARK(repItems(cons(z0, z1))) -> c27(A__REPITEMS(cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(repItems(pairNs)) -> c27(A__REPITEMS(a__pairNs)) MARK(repItems(s(z0))) -> c27(MARK(s(z0))) MARK(repItems(pair(z0, z1))) -> c27(MARK(pair(z0, z1))) A__ODDNS -> c2(A__INCR(cons(0, incr(oddNs)))) MARK(incr(incr(pairNs))) -> c20(A__INCR(a__incr(a__pairNs)), MARK(incr(pairNs))) MARK(incr(incr(incr(z0)))) -> c20(A__INCR(a__incr(a__incr(mark(z0)))), MARK(incr(incr(z0)))) MARK(incr(incr(oddNs))) -> c20(A__INCR(a__incr(a__oddNs)), MARK(incr(oddNs))) MARK(incr(incr(take(z0, z1)))) -> c20(A__INCR(a__incr(a__take(mark(z0), mark(z1)))), MARK(incr(take(z0, z1)))) MARK(incr(incr(zip(z0, z1)))) -> c20(A__INCR(a__incr(a__zip(mark(z0), mark(z1)))), MARK(incr(zip(z0, z1)))) MARK(incr(incr(tail(z0)))) -> c20(A__INCR(a__incr(a__tail(mark(z0)))), MARK(incr(tail(z0)))) MARK(incr(incr(repItems(z0)))) -> c20(A__INCR(a__incr(a__repItems(mark(z0)))), MARK(incr(repItems(z0)))) MARK(incr(incr(cons(z0, z1)))) -> c20(A__INCR(a__incr(cons(mark(z0), z1))), MARK(incr(cons(z0, z1)))) MARK(incr(incr(s(z0)))) -> c20(A__INCR(a__incr(s(mark(z0)))), MARK(incr(s(z0)))) MARK(incr(incr(pair(z0, z1)))) -> c20(A__INCR(a__incr(pair(mark(z0), mark(z1)))), MARK(incr(pair(z0, z1)))) MARK(incr(incr(x0))) -> c20(MARK(incr(x0))) MARK(incr(incr(0))) -> c20(A__INCR(a__incr(0))) MARK(incr(incr(nil))) -> c20(A__INCR(a__incr(nil))) MARK(incr(oddNs)) -> c20(A__INCR(a__incr(a__pairNs)), MARK(oddNs)) MARK(incr(oddNs)) -> c20(MARK(oddNs)) MARK(incr(take(x0, pairNs))) -> c20(A__INCR(a__take(mark(x0), a__pairNs)), MARK(take(x0, pairNs))) MARK(incr(take(x0, incr(z0)))) -> c20(A__INCR(a__take(mark(x0), a__incr(mark(z0)))), MARK(take(x0, incr(z0)))) MARK(incr(take(x0, oddNs))) -> c20(A__INCR(a__take(mark(x0), a__oddNs)), MARK(take(x0, oddNs))) MARK(incr(take(x0, take(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__take(mark(z0), mark(z1)))), MARK(take(x0, take(z0, z1)))) MARK(incr(take(x0, zip(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(take(x0, zip(z0, z1)))) MARK(incr(take(x0, tail(z0)))) -> c20(A__INCR(a__take(mark(x0), a__tail(mark(z0)))), MARK(take(x0, tail(z0)))) MARK(incr(take(x0, repItems(z0)))) -> c20(A__INCR(a__take(mark(x0), a__repItems(mark(z0)))), MARK(take(x0, repItems(z0)))) MARK(incr(take(x0, cons(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), cons(mark(z0), z1))), MARK(take(x0, cons(z0, z1)))) MARK(incr(take(x0, 0))) -> c20(A__INCR(a__take(mark(x0), 0)), MARK(take(x0, 0))) MARK(incr(take(x0, s(z0)))) -> c20(A__INCR(a__take(mark(x0), s(mark(z0)))), MARK(take(x0, s(z0)))) MARK(incr(take(x0, nil))) -> c20(A__INCR(a__take(mark(x0), nil)), MARK(take(x0, nil))) MARK(incr(take(x0, pair(z0, z1)))) -> c20(A__INCR(a__take(mark(x0), pair(mark(z0), mark(z1)))), MARK(take(x0, pair(z0, z1)))) MARK(incr(take(pairNs, x1))) -> c20(A__INCR(a__take(a__pairNs, mark(x1))), MARK(take(pairNs, x1))) MARK(incr(take(incr(z0), x1))) -> c20(A__INCR(a__take(a__incr(mark(z0)), mark(x1))), MARK(take(incr(z0), x1))) MARK(incr(take(oddNs, x1))) -> c20(A__INCR(a__take(a__oddNs, mark(x1))), MARK(take(oddNs, x1))) MARK(incr(take(take(z0, z1), x1))) -> c20(A__INCR(a__take(a__take(mark(z0), mark(z1)), mark(x1))), MARK(take(take(z0, z1), x1))) MARK(incr(take(zip(z0, z1), x1))) -> c20(A__INCR(a__take(a__zip(mark(z0), mark(z1)), mark(x1))), MARK(take(zip(z0, z1), x1))) MARK(incr(take(tail(z0), x1))) -> c20(A__INCR(a__take(a__tail(mark(z0)), mark(x1))), MARK(take(tail(z0), x1))) MARK(incr(take(repItems(z0), x1))) -> c20(A__INCR(a__take(a__repItems(mark(z0)), mark(x1))), MARK(take(repItems(z0), x1))) MARK(incr(take(cons(z0, z1), x1))) -> c20(A__INCR(a__take(cons(mark(z0), z1), mark(x1))), MARK(take(cons(z0, z1), x1))) MARK(incr(take(0, x1))) -> c20(A__INCR(a__take(0, mark(x1))), MARK(take(0, x1))) MARK(incr(take(s(z0), x1))) -> c20(A__INCR(a__take(s(mark(z0)), mark(x1))), MARK(take(s(z0), x1))) MARK(incr(take(nil, x1))) -> c20(A__INCR(a__take(nil, mark(x1))), MARK(take(nil, x1))) MARK(incr(take(pair(z0, z1), x1))) -> c20(A__INCR(a__take(pair(mark(z0), mark(z1)), mark(x1))), MARK(take(pair(z0, z1), x1))) MARK(incr(take(x0, x1))) -> c20(MARK(take(x0, x1))) MARK(incr(zip(x0, pairNs))) -> c20(A__INCR(a__zip(mark(x0), a__pairNs)), MARK(zip(x0, pairNs))) MARK(incr(zip(x0, incr(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__incr(mark(z0)))), MARK(zip(x0, incr(z0)))) MARK(incr(zip(x0, oddNs))) -> c20(A__INCR(a__zip(mark(x0), a__oddNs)), MARK(zip(x0, oddNs))) MARK(incr(zip(x0, take(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__take(mark(z0), mark(z1)))), MARK(zip(x0, take(z0, z1)))) MARK(incr(zip(x0, zip(z0, z1)))) -> c20(A__INCR(a__zip(mark(x0), a__zip(mark(z0), mark(z1)))), MARK(zip(x0, zip(z0, z1)))) MARK(incr(zip(x0, tail(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__tail(mark(z0)))), MARK(zip(x0, tail(z0)))) MARK(incr(zip(x0, repItems(z0)))) -> c20(A__INCR(a__zip(mark(x0), a__repItems(mark(z0)))), MARK(zip(x0, 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c23(A__TAKE(mark(x0), a__zip(0, mark(x2))), MARK(zip(0, x2))) MARK(take(x0, zip(s(z0), x2))) -> c23(A__TAKE(mark(x0), a__zip(s(mark(z0)), mark(x2))), MARK(zip(s(z0), x2))) MARK(take(x0, zip(nil, x2))) -> c23(A__TAKE(mark(x0), a__zip(nil, mark(x2))), MARK(zip(nil, x2))) MARK(take(x0, zip(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), a__zip(pair(mark(z0), mark(z1)), mark(x2))), MARK(zip(pair(z0, z1), x2))) MARK(take(pairNs, zip(x1, x2))) -> c23(A__TAKE(a__pairNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(incr(z0), zip(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(oddNs, zip(x1, x2))) -> c23(A__TAKE(a__oddNs, a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(take(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(zip(z0, z1), zip(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(tail(z0), zip(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(repItems(z0), zip(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(s(z0), zip(x1, x2))) -> c23(A__TAKE(s(mark(z0)), a__zip(mark(x1), mark(x2))), MARK(zip(x1, x2))) MARK(take(x0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(cons(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(0, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(nil, zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(pair(z0, z1), zip(x1, x2))) -> c23(MARK(zip(x1, x2))) MARK(take(x0, tail(pairNs))) -> c23(A__TAKE(mark(x0), a__tail(a__pairNs)), MARK(tail(pairNs))) MARK(take(x0, tail(incr(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__incr(mark(z0)))), MARK(tail(incr(z0)))) MARK(take(x0, tail(oddNs))) -> c23(A__TAKE(mark(x0), a__tail(a__oddNs)), MARK(tail(oddNs))) MARK(take(x0, tail(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__take(mark(z0), mark(z1)))), MARK(tail(take(z0, z1)))) MARK(take(x0, tail(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(a__zip(mark(z0), mark(z1)))), MARK(tail(zip(z0, z1)))) MARK(take(x0, tail(tail(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__tail(mark(z0)))), MARK(tail(tail(z0)))) MARK(take(x0, tail(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__tail(a__repItems(mark(z0)))), MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), 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MARK(take(incr(cons(z0, z1)), x1)) -> c23(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(incr(0), x1)) -> c23(A__TAKE(a__incr(0), mark(x1)), MARK(x1)) MARK(take(incr(s(z0)), x1)) -> c23(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(nil), x1)) -> c23(A__TAKE(a__incr(nil), mark(x1)), MARK(x1)) MARK(take(incr(pair(z0, z1)), x1)) -> c23(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(x0), pairNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__pairNs)) MARK(take(incr(x0), s(z0))) -> c23(MARK(s(z0))) MARK(take(incr(x0), pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(incr(x0), x1)) -> c23(MARK(x1)) S tuples: A__INCR(cons(z0, z1)) -> c4(MARK(z0)) A__TAKE(s(z0), cons(z1, z2)) -> c7(MARK(z1)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c11(MARK(z0)) A__ZIP(cons(z0, z1), cons(z2, z3)) -> c12(MARK(z2)) A__TAIL(cons(z0, z1)) -> c14(MARK(z1)) A__REPITEMS(cons(z0, z1)) -> c17(MARK(z0)) MARK(oddNs) -> c21(A__ODDNS) MARK(cons(z0, z1)) -> 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MARK(tail(repItems(z0)))) MARK(take(x0, tail(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(cons(mark(z0), z1))), MARK(tail(cons(z0, z1)))) MARK(take(x0, tail(s(z0)))) -> c23(A__TAKE(mark(x0), a__tail(s(mark(z0)))), MARK(tail(s(z0)))) MARK(take(x0, tail(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__tail(pair(mark(z0), mark(z1)))), MARK(tail(pair(z0, z1)))) MARK(take(pairNs, tail(x1))) -> c23(A__TAKE(a__pairNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(incr(z0), tail(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(oddNs, tail(x1))) -> c23(A__TAKE(a__oddNs, a__tail(mark(x1))), MARK(tail(x1))) MARK(take(take(z0, z1), tail(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(zip(z0, z1), tail(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(tail(z0), tail(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(repItems(z0), tail(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(s(z0), tail(x1))) -> c23(A__TAKE(s(mark(z0)), a__tail(mark(x1))), MARK(tail(x1))) MARK(take(x0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, tail(0))) -> c23(A__TAKE(mark(x0), a__tail(0))) MARK(take(x0, tail(nil))) -> c23(A__TAKE(mark(x0), a__tail(nil))) MARK(take(cons(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(0, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(nil, tail(x1))) -> c23(MARK(tail(x1))) MARK(take(pair(z0, z1), tail(x1))) -> c23(MARK(tail(x1))) MARK(take(x0, repItems(pairNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__pairNs)), MARK(repItems(pairNs))) MARK(take(x0, repItems(incr(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__incr(mark(z0)))), MARK(repItems(incr(z0)))) MARK(take(x0, repItems(oddNs))) -> c23(A__TAKE(mark(x0), a__repItems(a__oddNs)), MARK(repItems(oddNs))) MARK(take(x0, repItems(take(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__take(mark(z0), mark(z1)))), MARK(repItems(take(z0, z1)))) MARK(take(x0, repItems(zip(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(a__zip(mark(z0), mark(z1)))), MARK(repItems(zip(z0, z1)))) MARK(take(x0, repItems(tail(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__tail(mark(z0)))), MARK(repItems(tail(z0)))) MARK(take(x0, repItems(repItems(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(a__repItems(mark(z0)))), MARK(repItems(repItems(z0)))) MARK(take(x0, repItems(cons(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(cons(mark(z0), z1))), MARK(repItems(cons(z0, z1)))) MARK(take(x0, repItems(s(z0)))) -> c23(A__TAKE(mark(x0), a__repItems(s(mark(z0)))), MARK(repItems(s(z0)))) MARK(take(x0, repItems(pair(z0, z1)))) -> c23(A__TAKE(mark(x0), a__repItems(pair(mark(z0), mark(z1)))), MARK(repItems(pair(z0, z1)))) MARK(take(pairNs, repItems(x1))) -> c23(A__TAKE(a__pairNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(incr(z0), repItems(x1))) -> c23(A__TAKE(a__incr(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(oddNs, repItems(x1))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(take(z0, z1), repItems(x1))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(zip(z0, z1), repItems(x1))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(tail(z0), repItems(x1))) -> c23(A__TAKE(a__tail(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(repItems(z0), repItems(x1))) -> c23(A__TAKE(a__repItems(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(s(z0), repItems(x1))) -> c23(A__TAKE(s(mark(z0)), a__repItems(mark(x1))), MARK(repItems(x1))) MARK(take(x0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, repItems(0))) -> c23(A__TAKE(mark(x0), a__repItems(0))) MARK(take(x0, repItems(nil))) -> c23(A__TAKE(mark(x0), a__repItems(nil))) MARK(take(cons(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(0, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(nil, repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(pair(z0, z1), repItems(x1))) -> c23(MARK(repItems(x1))) MARK(take(x0, cons(pairNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__pairNs, x2)), MARK(cons(pairNs, x2))) MARK(take(x0, cons(incr(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__incr(mark(z0)), x2)), MARK(cons(incr(z0), x2))) MARK(take(x0, cons(oddNs, x2))) -> c23(A__TAKE(mark(x0), cons(a__oddNs, x2)), MARK(cons(oddNs, x2))) MARK(take(x0, cons(take(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__take(mark(z0), mark(z1)), x2)), MARK(cons(take(z0, z1), x2))) MARK(take(x0, cons(zip(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(a__zip(mark(z0), mark(z1)), x2)), MARK(cons(zip(z0, z1), x2))) MARK(take(x0, cons(tail(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__tail(mark(z0)), x2)), MARK(cons(tail(z0), x2))) MARK(take(x0, cons(repItems(z0), x2))) -> c23(A__TAKE(mark(x0), cons(a__repItems(mark(z0)), x2)), MARK(cons(repItems(z0), x2))) MARK(take(x0, cons(cons(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(cons(mark(z0), z1), x2)), MARK(cons(cons(z0, z1), x2))) MARK(take(x0, cons(0, x2))) -> c23(A__TAKE(mark(x0), cons(0, x2)), MARK(cons(0, x2))) MARK(take(x0, cons(s(z0), x2))) -> c23(A__TAKE(mark(x0), cons(s(mark(z0)), x2)), MARK(cons(s(z0), x2))) MARK(take(x0, cons(nil, x2))) -> c23(A__TAKE(mark(x0), cons(nil, x2)), MARK(cons(nil, x2))) MARK(take(x0, cons(pair(z0, z1), x2))) -> c23(A__TAKE(mark(x0), cons(pair(mark(z0), mark(z1)), x2)), MARK(cons(pair(z0, z1), x2))) MARK(take(pairNs, cons(x1, x2))) -> c23(A__TAKE(a__pairNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(incr(z0), cons(x1, x2))) -> c23(A__TAKE(a__incr(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(oddNs, cons(x1, x2))) -> c23(A__TAKE(a__oddNs, cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(take(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__take(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(zip(z0, z1), cons(x1, x2))) -> c23(A__TAKE(a__zip(mark(z0), mark(z1)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(tail(z0), cons(x1, x2))) -> c23(A__TAKE(a__tail(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(repItems(z0), cons(x1, x2))) -> c23(A__TAKE(a__repItems(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(s(z0), cons(x1, x2))) -> c23(A__TAKE(s(mark(z0)), cons(mark(x1), x2)), MARK(cons(x1, x2))) MARK(take(x0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(cons(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(0, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(nil, cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pair(z0, z1), cons(x1, x2))) -> c23(MARK(cons(x1, x2))) MARK(take(pairNs, pairNs)) -> c23(A__TAKE(a__pairNs, a__pairNs)) MARK(take(pairNs, s(z0))) -> c23(MARK(s(z0))) MARK(take(pairNs, pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(pairNs, x0)) -> c23(MARK(x0)) MARK(take(incr(pairNs), x1)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x1)), MARK(x1)) MARK(take(incr(incr(z0)), x1)) -> c23(A__TAKE(a__incr(a__incr(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(oddNs), x1)) -> c23(A__TAKE(a__incr(a__oddNs), mark(x1)), MARK(x1)) MARK(take(incr(take(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__take(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(zip(z0, z1)), x1)) -> c23(A__TAKE(a__incr(a__zip(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(tail(z0)), x1)) -> c23(A__TAKE(a__incr(a__tail(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(repItems(z0)), x1)) -> c23(A__TAKE(a__incr(a__repItems(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(cons(z0, z1)), x1)) -> c23(A__TAKE(a__incr(cons(mark(z0), z1)), mark(x1)), MARK(x1)) MARK(take(incr(0), x1)) -> c23(A__TAKE(a__incr(0), mark(x1)), MARK(x1)) MARK(take(incr(s(z0)), x1)) -> c23(A__TAKE(a__incr(s(mark(z0))), mark(x1)), MARK(x1)) MARK(take(incr(nil), x1)) -> c23(A__TAKE(a__incr(nil), mark(x1)), MARK(x1)) MARK(take(incr(pair(z0, z1)), x1)) -> c23(A__TAKE(a__incr(pair(mark(z0), mark(z1))), mark(x1)), MARK(x1)) MARK(take(incr(x0), pairNs)) -> c23(A__TAKE(a__incr(mark(x0)), a__pairNs)) MARK(take(incr(x0), s(z0))) -> c23(MARK(s(z0))) MARK(take(incr(x0), pair(z0, z1))) -> c23(MARK(pair(z0, z1))) MARK(take(incr(x0), x1)) -> c23(MARK(x1)) K tuples:none Defined Rule Symbols: a__pairNs, a__oddNs, a__incr_1, a__take_2, a__zip_2, a__tail_1, a__repItems_1, mark_1 Defined Pair Symbols: A__INCR_1, A__TAKE_2, A__ZIP_2, A__TAIL_1, A__REPITEMS_1, MARK_1, A__ODDNS Compound Symbols: c4_1, c7_1, c11_1, c12_1, c14_1, c17_1, c21_1, c28_1, c30_1, c32_1, c33_1, c20_2, c20_1, c22_1, c23_2, c23_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c2_1, c22_2