KILLED proof of input_mHYMHnjTgt.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 116 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) InliningProof [UPPER BOUND(ID), 213 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) CompletionProof [UPPER BOUND(ID), 0 ms] (20) CpxTypedWeightedCompleteTrs (21) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (24) CdtProblem (25) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (54) CdtProblem (55) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms] (60) CdtProblem (61) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 7 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms] (84) CdtProblem (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (100) CdtProblem (101) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 66 ms] (104) CdtProblem (105) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 99 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 19 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 178 ms] (122) CdtProblem (123) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 206 ms] (128) CdtProblem (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 14 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 141 ms] (134) CdtProblem (135) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 208 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 215 ms] (146) CdtProblem (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 36 ms] (148) CdtProblem (149) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 133 ms] (152) CdtProblem (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 75 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 21 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 353 ms] (160) CdtProblem (161) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 75 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 218 ms] (164) CdtProblem (165) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 30 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 156 ms] (168) CdtProblem (169) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 28 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 131 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 26 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 155 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 48 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 146 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 43 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 234 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 116 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 60 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 438 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 97 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 320 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 37 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 279 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 52 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 232 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 12 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 213 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 59 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 327 ms] (212) CdtProblem (213) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 116 ms] (214) CdtProblem (215) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 117 ms] (216) CdtProblem (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 546 ms] (218) CdtProblem (219) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 135 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 63 ms] (222) CdtProblem (223) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 297 ms] (224) CdtProblem (225) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 106 ms] (226) 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) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (6) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__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 ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (9) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__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 ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (11) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__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 ---------------------------------------- (13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 oddNs => 2 nil => 1 pairNs => 3 ---------------------------------------- (14) 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 ---------------------------------------- (15) 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) :|: ---------------------------------------- (16) 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 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) 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 ---------------------------------------- (19) 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 ---------------------------------------- (20) 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 ---------------------------------------- (21) 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 ---------------------------------------- (22) 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. ---------------------------------------- (23) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (24) 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 ---------------------------------------- (25) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 15 trailing nodes: MARK(0) -> c29 A__TAIL(z0) -> c15 A__ZIP(nil, z0) -> c9 A__INCR(z0) -> c5 A__ODDNS -> c3 A__REPITEMS(z0) -> c18 MARK(nil) -> c31 A__ZIP(z0, z1) -> c13 A__ZIP(z0, nil) -> c10 A__PAIRNS -> c1 A__REPITEMS(nil) -> c16 A__TAKE(z0, z1) -> c8 A__TAKE(0, z0) -> c6 A__PAIRNS -> c MARK(pairNs) -> c19(A__PAIRNS) ---------------------------------------- (26) 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 ---------------------------------------- (27) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (28) 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 ---------------------------------------- (29) 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))) ---------------------------------------- (30) 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 ---------------------------------------- (31) 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)) ---------------------------------------- (32) 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 ---------------------------------------- (33) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (34) 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 ---------------------------------------- (35) 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))) ---------------------------------------- (36) 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 ---------------------------------------- (37) 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)) ---------------------------------------- (38) 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 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (40) 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 ---------------------------------------- (41) 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)) ---------------------------------------- (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__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 ---------------------------------------- (43) 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)) ---------------------------------------- (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__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 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 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(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 ---------------------------------------- (47) 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))) ---------------------------------------- (48) 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 ---------------------------------------- (49) 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)) ---------------------------------------- (50) 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 ---------------------------------------- (51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (52) 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 ---------------------------------------- (53) 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)) ---------------------------------------- (54) 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 ---------------------------------------- (55) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(zip(x0, nil)) -> c25(A__ZIP(mark(x0), nil), MARK(nil)) MARK(zip(x0, 0)) -> c25(A__ZIP(mark(x0), 0), MARK(0)) ---------------------------------------- (56) 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 ---------------------------------------- (57) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (58) 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 ---------------------------------------- (59) 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))) ---------------------------------------- (60) 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 ---------------------------------------- (61) 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)) ---------------------------------------- (62) 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 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (64) 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 ---------------------------------------- (65) 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))) ---------------------------------------- (66) 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 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(repItems(nil)) -> c27(A__REPITEMS(nil), MARK(nil)) MARK(repItems(0)) -> c27(A__REPITEMS(0), MARK(0)) ---------------------------------------- (68) 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 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (71) 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)) ---------------------------------------- (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(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 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__ODDNS -> c2(A__INCR(pairNs)) ---------------------------------------- (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(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 ---------------------------------------- (75) 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)))) ---------------------------------------- (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(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 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (79) 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)) ---------------------------------------- (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(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 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (83) 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))) ---------------------------------------- (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(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 ---------------------------------------- (85) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 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(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, 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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 ---------------------------------------- (87) 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))) ---------------------------------------- (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(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))) 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 ---------------------------------------- (89) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (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(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))) 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 ---------------------------------------- (91) 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)))) ---------------------------------------- (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(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), 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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)))) 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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), 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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 ---------------------------------------- (93) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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(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)) -> 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, 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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), 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 ---------------------------------------- (95) 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)))) ---------------------------------------- (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(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), 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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 ---------------------------------------- (97) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 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(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 ---------------------------------------- (99) 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)) ---------------------------------------- (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(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 ---------------------------------------- (101) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(incr(pairNs)) -> c20(A__INCR(pairNs)) ---------------------------------------- (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(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, 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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)))) 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 ---------------------------------------- (103) 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))) ---------------------------------------- (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(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)), 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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, 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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 ---------------------------------------- (105) 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)) ---------------------------------------- (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)) 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(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))) 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(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 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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)) 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), 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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, 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 ---------------------------------------- (109) 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))) ---------------------------------------- (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)) 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, 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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)))), 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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, 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))) 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)) -> 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(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 ---------------------------------------- (111) 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)) ---------------------------------------- (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(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)) -> 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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))) 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)) -> 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(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 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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)))) 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), 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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))) 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)) -> 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))) 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(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))) ---------------------------------------- (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(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))) -> 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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 ---------------------------------------- (117) 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)) ---------------------------------------- (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(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, 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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, 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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 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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 ---------------------------------------- (121) 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))) ---------------------------------------- (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(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))) -> 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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)))), 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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))) 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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(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), 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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))) 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))) -> 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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 ---------------------------------------- (123) 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)) ---------------------------------------- (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(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)), 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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))) 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))) 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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 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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(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))) 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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))) 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, 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 ---------------------------------------- (127) 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))) ---------------------------------------- (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(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)))) -> 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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))) 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)))), 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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), 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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 ---------------------------------------- (129) 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)) ---------------------------------------- (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(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))) 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))) 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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(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 ---------------------------------------- (131) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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)) -> 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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), 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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)))) -> 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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))), 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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, 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 ---------------------------------------- (133) 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))) ---------------------------------------- (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(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)), 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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))) 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)) -> 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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 ---------------------------------------- (135) 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)) ---------------------------------------- (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(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), 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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(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))) -> 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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(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 ---------------------------------------- (137) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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(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), 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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))) 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)), 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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 ---------------------------------------- (139) 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))) ---------------------------------------- (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, 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)))) 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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)), 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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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 ---------------------------------------- (141) 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)) ---------------------------------------- (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, 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))) -> 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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(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))), 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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 ---------------------------------------- (143) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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, 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)))) -> 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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))) 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)), 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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(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(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 ---------------------------------------- (145) 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))) ---------------------------------------- (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(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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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(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)) -> 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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(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 ---------------------------------------- (147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(nil, cons(x1, x2))) -> c22(A__TAKE(nil, cons(mark(x1), x2)), MARK(nil)) MARK(take(0, cons(x1, x2))) -> c22(A__TAKE(0, cons(mark(x1), x2)), MARK(0)) ---------------------------------------- (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(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)))) -> 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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(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)))) -> 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__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 ---------------------------------------- (149) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (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(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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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)), 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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, 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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, 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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))), 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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)) 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)))) 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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 ---------------------------------------- (151) 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)))) ---------------------------------------- (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(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), 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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))) 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, 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, 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))) 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 ---------------------------------------- (153) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 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(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), 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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))) 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)) -> 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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 ---------------------------------------- (155) 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)) ---------------------------------------- (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(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)))) -> 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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, 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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))) -> 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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))) 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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)) -> 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)), 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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), 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, 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 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(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, 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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))) -> 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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))) 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, 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))) 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 ---------------------------------------- (159) 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))) ---------------------------------------- (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(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)))) -> 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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))) -> 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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)) 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))) 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)) -> 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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 ---------------------------------------- (161) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(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)))), 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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)) 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)))) -> 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-> 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)) 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 ---------------------------------------- (163) 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))) ---------------------------------------- (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(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))) 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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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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)) -> 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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 ---------------------------------------- (165) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(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), 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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))) 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))) 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)) 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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)) -> 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))) 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(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)))) ---------------------------------------- (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(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))), 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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)) -> 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)), 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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 ---------------------------------------- (169) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (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(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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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))) 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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))) 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)) 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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))) 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) 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)))) ---------------------------------------- (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(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))), 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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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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, 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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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)))) 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) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (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(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, 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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))) 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)))), 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)))) -> 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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))) 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) 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))) ---------------------------------------- (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, 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)) -> 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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 ---------------------------------------- (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, 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), 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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(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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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))) 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))) -> 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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))) 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 ---------------------------------------- (179) 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))) ---------------------------------------- (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, 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), 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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(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))) 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, 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)) -> 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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), 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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(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 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: 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, nil)) -> c22(A__TAKE(a__pairNs, nil)) MARK(take(pairNs, s(z0))) -> c22(A__TAKE(a__pairNs, s(mark(z0)))) MARK(take(pairNs, x0)) -> c22(A__TAKE(pairNs, mark(x0))) MARK(take(pairNs, x0)) -> c22(A__TAKE(cons(0, incr(oddNs)), mark(x0))) ---------------------------------------- (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, 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, 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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))) 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, 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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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))) -> 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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(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)))) -> 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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, 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))) 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 ---------------------------------------- (183) 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))) ---------------------------------------- (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, 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))) 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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)) -> 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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)), 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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, 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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 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (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(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, 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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 ---------------------------------------- (187) 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)) ---------------------------------------- (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(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, 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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(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)) -> 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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, 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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(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 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(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, 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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)) 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))) 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)))) 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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(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 ---------------------------------------- (191) 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))) ---------------------------------------- (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(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))) -> 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)))) -> 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-> 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))) -> 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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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)), 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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, 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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 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 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(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))) -> 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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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)), 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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))) -> 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))) 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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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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(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 ---------------------------------------- (195) 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))) ---------------------------------------- (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(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)))) -> 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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(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)), 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))) 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)) -> 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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, 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))) 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 ---------------------------------------- (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(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)) -> 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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)) 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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), 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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, 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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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 ---------------------------------------- (199) 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))) ---------------------------------------- (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(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), 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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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 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 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(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), 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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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, 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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, 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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))) 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))) -> 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))) 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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)))) 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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, 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))) 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 ---------------------------------------- (203) 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))) ---------------------------------------- (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(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))) -> 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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)) -> 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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(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))) 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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)) -> 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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)), 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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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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 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 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(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))) -> 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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)), 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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))), 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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 ---------------------------------------- (207) 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))) ---------------------------------------- (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(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))) -> 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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))) 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)), 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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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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))), 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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(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 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 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(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))) -> 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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 ---------------------------------------- (211) 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)) ---------------------------------------- (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(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), 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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(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))) -> 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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)) 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(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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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))) 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 ---------------------------------------- (213) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(pairNs, nil)) -> c23(A__TAKE(a__pairNs, nil), MARK(nil)) MARK(take(pairNs, 0)) -> c23(A__TAKE(a__pairNs, 0), MARK(0)) ---------------------------------------- (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(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), 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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 ---------------------------------------- (215) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (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(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))) -> 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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)) 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(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)), 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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, 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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(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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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, 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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)) 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) 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)) ---------------------------------------- (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(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)))), 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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))) -> 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))) -> 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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), 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 ---------------------------------------- (219) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(incr(x0), nil)) -> c23(A__TAKE(a__incr(mark(x0)), nil), MARK(nil)) MARK(take(incr(x0), 0)) -> c23(A__TAKE(a__incr(mark(x0)), 0), MARK(0)) ---------------------------------------- (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(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))) -> 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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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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 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (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(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__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)) 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))) -> 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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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 ---------------------------------------- (223) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(take(oddNs, x1)) -> c23(A__TAKE(a__oddNs, mark(x1)), MARK(x1)) by MARK(take(oddNs, pairNs)) -> c23(A__TAKE(a__oddNs, a__pairNs), MARK(pairNs)) MARK(take(oddNs, incr(z0))) -> c23(A__TAKE(a__oddNs, a__incr(mark(z0))), MARK(incr(z0))) MARK(take(oddNs, oddNs)) -> c23(A__TAKE(a__oddNs, a__oddNs), MARK(oddNs)) MARK(take(oddNs, take(z0, z1))) -> c23(A__TAKE(a__oddNs, a__take(mark(z0), mark(z1))), MARK(take(z0, z1))) MARK(take(oddNs, zip(z0, z1))) -> c23(A__TAKE(a__oddNs, a__zip(mark(z0), mark(z1))), MARK(zip(z0, z1))) MARK(take(oddNs, tail(z0))) -> c23(A__TAKE(a__oddNs, a__tail(mark(z0))), MARK(tail(z0))) MARK(take(oddNs, repItems(z0))) -> c23(A__TAKE(a__oddNs, a__repItems(mark(z0))), MARK(repItems(z0))) MARK(take(oddNs, cons(z0, z1))) -> c23(A__TAKE(a__oddNs, cons(mark(z0), z1)), MARK(cons(z0, z1))) MARK(take(oddNs, 0)) -> c23(A__TAKE(a__oddNs, 0), MARK(0)) MARK(take(oddNs, s(z0))) -> c23(A__TAKE(a__oddNs, s(mark(z0))), MARK(s(z0))) MARK(take(oddNs, nil)) -> c23(A__TAKE(a__oddNs, nil), MARK(nil)) MARK(take(oddNs, pair(z0, z1))) -> c23(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(oddNs, x0)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(x0)) MARK(take(oddNs, x0)) -> c23(A__TAKE(oddNs, mark(x0)), MARK(x0)) ---------------------------------------- (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(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))) 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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)) MARK(take(oddNs, pairNs)) -> c23(A__TAKE(a__oddNs, a__pairNs), MARK(pairNs)) MARK(take(oddNs, 0)) -> c23(A__TAKE(a__oddNs, 0), MARK(0)) MARK(take(oddNs, s(z0))) -> c23(A__TAKE(a__oddNs, s(mark(z0))), MARK(s(z0))) MARK(take(oddNs, nil)) -> c23(A__TAKE(a__oddNs, nil), MARK(nil)) MARK(take(oddNs, pair(z0, z1))) -> c23(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(oddNs, x0)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(x0)) MARK(take(oddNs, x0)) -> c23(A__TAKE(oddNs, 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), x1)) -> c22(MARK(pair(z0, z1))) 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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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(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)) MARK(take(oddNs, pairNs)) -> c23(A__TAKE(a__oddNs, a__pairNs), MARK(pairNs)) MARK(take(oddNs, 0)) -> c23(A__TAKE(a__oddNs, 0), MARK(0)) MARK(take(oddNs, s(z0))) -> c23(A__TAKE(a__oddNs, s(mark(z0))), MARK(s(z0))) MARK(take(oddNs, nil)) -> c23(A__TAKE(a__oddNs, nil), MARK(nil)) MARK(take(oddNs, pair(z0, z1))) -> c23(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(oddNs, x0)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(x0)) MARK(take(oddNs, x0)) -> c23(A__TAKE(oddNs, 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 ---------------------------------------- (225) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: MARK(take(oddNs, nil)) -> c23(A__TAKE(a__oddNs, nil), MARK(nil)) MARK(take(oddNs, 0)) -> c23(A__TAKE(a__oddNs, 0), MARK(0)) ---------------------------------------- (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(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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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)))) -> 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-> 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(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)) MARK(take(oddNs, pairNs)) -> c23(A__TAKE(a__oddNs, a__pairNs), MARK(pairNs)) MARK(take(oddNs, s(z0))) -> c23(A__TAKE(a__oddNs, s(mark(z0))), MARK(s(z0))) MARK(take(oddNs, pair(z0, z1))) -> c23(A__TAKE(a__oddNs, pair(mark(z0), mark(z1))), MARK(pair(z0, z1))) MARK(take(oddNs, x0)) -> c23(A__TAKE(a__incr(a__pairNs), mark(x0)), MARK(x0)) MARK(take(oddNs, x0)) -> c23(A__TAKE(oddNs, 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